x² + 6x + 8 = 0 Completing the Square. Created by RizaClaireeee. Math

x² + 6x + 8 = 0 Completing the Square...

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October 2022 1 2 Report

x² + 6x + 8 = 0 Completing the Square

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KAntoineDoix

Verified answer

✒️QUADRATIC

$••••••••••••••••••••••••••••••••••••••••••••••••••$

$\large\underline{\mathbb{ANSWER}:}$

$\qquad \LARGE \:\: \rm \text-2 \; and \; \text-4$

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$\large\underline{\mathbb{SOLUTION}:}$

Rewrite the standard form of the quadratic equation into:

$ax^2 + bx = \text-c$

$x^2 + 6x = \text-8$

Add (b/2)² to both sides of the equation.

$x^2 + 6x + (6/2)^2 = \text-8 + (6/2)^2$

$x^2 + 6x + (3)^2 = \text-8 + (3)^2$

$x^2 + 6x + 9 = \text-8 + 9$

Complete the square then add the two terms on the right.

$(x + 3)^2 = 1$

$\sqrt{(x+3)^2\,} = \pm\,\sqrt1$

$x + 3 = \pm\,1$

Separate the equation into two solutions then find the values of x.

$x + 3 = 1 \quad;\quad x + 3 = \text-1$

$x = 1 - 3 \quad;\quad x = \text-1 - 3$

$x = \text-2 \quad;\quad x = \text-4$

Therefore, the solutions after solving by completing the square are -2 and -4

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✒️QUADRATIC

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