Step #4 – Last step is to set the equation to zero by using subtraction 2x 2 + 20x + 8 = 0 This is due to the fact that you are splitting that term into two parts. Your new perfect square, the h, is the b term divided by two. What you do to one side, you do to the other side. This number gets added to both sides of the equation to maintain the balance of the equation. This is done by first dividing the b term by 2 and squaring the quotient. Step #2 – Use the b term in order to find a new c term that makes a perfect square.
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Step #1 – Move the c term to the other side of the equation using addition. The first example is going to be done with the equation from above since it has a coefficient of 1 so a = 1. Solve by Completing the Square Examples Example When you complete the square you can get the equation (x+3) 2 – 17 = 0. The maximum height of the ball or when the ball it’s the ground would be answers that could be found when the equation is in vertex form. The completing the square formula is calculated by converting the left side of a quadratic equation to a perfect square trinomial.įor example, if a ball is thrown and it follows the path of the completing the square equation x 2 + 6x – 8 = 0. Find your h, the b term divided by two, for the perfect square.This is done by first dividing the b term by 2 and squaring the quotient and add to both sides of the equation. Use the b term in order to find a new c term that makes a perfect square.Move the c term to the other side of the equation.
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Here are the completing the square steps and operations to solve a quadratic equation in algebra. It also helps to find the vertex (h, k) which would be the maximum or minimum of the equation. The vertex form is much easier to solve or find the zeros of quadratic equations than the standard form equation.
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Don't wait until the answer in the back of the book "reminds" you that you "meant" to put the square root symbol in there. On the same note, make sure you draw in the square root sign, as necessary, when you square root both sides. Besides, there's no reason to go ticking off your instructor by doing something wrong when it's so simple to do it right. On your tests, you won't have the answers in the back to "remind" you that you "meant" to use the plus-minus, and you will likely forget to put the plus-minus into the answer. If you lose the sign from that term, you can get the wrong answer in the end because you'll forget which sign goes inside the parentheses in the completed-square form.Īlso, don't be sloppy and wait to do the plus/minus sign until the very end. When you complete the square, make sure that you are careful with the sign on the numerical coefficient of the x-term when you multiply that coefficient by one-half. But (warning!) in most other cases, you should assume that the answer should be in "exact" form, complete with all the square roots. For instance, for the above exercise, it's a lot easier to graph an intercept at x = -0.9 than it is to try to graph the number in square-root form with a "minus" in the middle. You will need probably rounded forms for "real life" answers to word problems, and for graphing.