Solving Quadratic Equations by Completing the Square Example 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. 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.
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