![]() The techniques we have encountered so far can be applied to word and practical problems in other areas of mathematics. The solution set of the given equation is. Solving each of these linear equations leads to We set each factor equal to 0, leading to If the product of three factors is equal to 0, at least one of the individual factors must be equal to 0. The fully factored form of the equation is therefore Is the difference of two squares and hence can be factored as follows: We observe that the quadratic expression □ − 9 We now have the product of a linear term and a quadratic expression. The equation can therefore be factored as We observe that the two terms on the left-hand side of the equation have a common factor of 2 □. This equation is of degree 3 and hence is a cubic equation. The equation we are given is not a quadratic equation. We summarize the steps involved in solving a quadratic equation by factoring in the process below.Įxample 3: Solving an Equation by First Identifying the Highest Common Factor between the Termsįind the solution set for 2 □ = 1 8 □ . We can check our answer by substituting □ = 4 back into the original quadratic equation: This is a repeated root, but we only need to list it once as our solution. We have a repeated factor of ( □ − 4 ), so we only have one equation to solve: ![]() To solve a quadratic equation in its factored form, we set each factor equal to 0 and then solve the resulting linear equations. The quadratic is, therefore, a perfect square. 16 is equal to 4 ,Īdditionally, we observe that the middle term, − 8 □, is equal to the negative of twice the square root of the first term multiplied Upon inspection, we observe that both the first and third terms in this quadratic equation are perfect squares. Solve the equation □ − 8 □ + 1 6 = 0 by factoring. In the next example, we will demonstrate how to solve a quadratic equation by first recognizing it as a perfect square and hence writing the quadratic in its factored form.Įxample 2: Solving a Simple Quadratic Equation by Factoring This can be expressed as the solution set − 4 3, 3 2 . The solutions to the quadratic equation ( 2 □ − 3 ) ( 3 □ + 4 ) = 0 are □ = 3 2 and The second equation can be solved by subtracting 4 from each side and then dividing by 3: The first equation can be solved by adding 3 to each side and then dividing by 2: We therefore have two linear equations to solve. The only way the product of these two expressions can be 0 is if one of the factors individually is equal to 0. We are given that the product of the two linear expressions ( 2 □ − 3 )Īnd ( 3 □ + 4 ) is 0. This quadratic equation is already in a factored form. In our first example, we will demonstrate the process of solving a quadratic equation given its factored form.Įxample 1: Solving a Prefactored Equation It is important to remember that not every quadratic equation is factorable, so the methods we discuss here can only be applied to those that are. In some cases, the two solutions may coincide to give one repeated root, in which case we only give this value once as the solution. There are therefore two solutions, or roots, to the given quadratic equation: □ = − □ □ and □ = − □ □. So, to find all solutions to the given equation, we set each factor equal to 0, leading to two linear equations: The key to solving such an equation is to recognize that if the product of two (or more) factors is equal to 0, then at least one of the individual factors Suppose we have a quadratic equation in its factored form, ![]() The focus of this explainer is the application of these skills to solving quadratic equations. recognizing a quadratic as the difference of two squares,.recognizing a quadratic as a perfect square,.We should already be familiar with a number of methods for factoring quadratic expressions, including We will learn how to solve these types of equations as we continue in our study of algebra.A quadratic equation is any equation that can be expressed in the form □ □ + □ □ + □ = 0 , where □, □, In fact, many polynomial equations that do not factor do have real solutions. This does not imply that equations involving these unfactorable polynomials do not have real solutions. We have seen that many polynomials do not factor. In general, for any polynomial equation with one variable of degree \(n\), the fundamental theorem of algebra guarantees \(n\) real solutions or fewer. Notice that the degree of the polynomial is \(3\) and we obtained three solutions.
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Sure, you can fill this space with hot, degrading words about how you're too small to please a real woman anyway (that kind of thing is always so fun to read), or you can talk about how much more energy and focus you have now that you're not allowed access to your clit. ![]() ![]() I encourage you to read some of the other posts while you're there, sweetie - see what other girls say about why chastity is important for them. Then, when you're done, you're going to post the writing for everybody in the discord server to read. You are going to write at least 100 words on why you need to be in chastity. So, this task is for your sisters-in-chasitity just as much as it is for yourself. Not you, though - you're a good girl.īut the temptation is always there. You might even be feeling tempted to finish your lockup already - I know a few of your fellow lockees have already dropped out. You're coming to the end of your first week of chastity, sissy - and I'm sure there's plenty to reflect on about how this week has been for you so far. If you're a seasoned chastity wearer, then your task for today is to log into the discord server and tell everybody one thing you've learned about wearing a cage. Some of the girls here have only just now spent a night in chastity for the first time. Then you're done, sissy girl! If you need any more advice, just ask in the discord server, and somebody will be along to help you out very soon.įor the more experienced chastity-sluts joining us for Locktober, I'm sure you have plenty of tips and tricks of your own to share. And you're going to wipe down your cage properly when you're done - the only spots I want to see on your panties are from your leaking prostate! If you notice your foreskin keeps getting trapped and pinched, think about pushing a little tissue paper into the tip of the cage to keep it from rubbing. I don't care if you can still pee standing up, sissy. If you're managing to find some magical way of still standing up to use the toilet, then I want you to change that habit now. For a lot of girls, that's the moment - the 'oh god' moment - when they realise they're not a real man anymore.Ĭhastity is a feminizing experience in many ways, sissy - and this is a big mindfuck to get used to. Even if you're new to chastity, you've probably realised by now that you have to sit down to use the toilet without squirting and spraying everywhere. |
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