How do you solve the quadratic equation by completing the square: $x^{2} + 18 x + 67 = 0$ $x^2+18x+67=0$ ?

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How do you solve the quadratic equation by completing the square: $x^{2} + 18 x + 67 = 0$ $x^2+18x+67=0$ ?

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Answer 1 · 2015-07-19T13:52:54

$x = \sqrt{14} - 9$ $color(green)(x = sqrt 14 -9$ or $x = - \sqrt{14} - 9$ $color(green)(x = -sqrt 14 -9$

Explanation:

$x^{2} + 18 x = - 67$ $x^2 + 18x = -67$

To write the Left Hand Side as a Perfect Square, we add 81 to both sides.

$x^{2} + 18 x + 81 = - 67 + 81$ $x^2 + 18x + 81 = -67 + 81$

$x^{2} + 2 \cdot x \cdot 9 + 9^{2} = 14$ $x^2 + 2*x*9 + 9^2 = 14$

Using the Identity ${(a + b)}^{2} = a^{2} + 2 a b + b^{2}$ $color(blue)((a+b)^2 = a^2 + 2ab + b^2$ , we get
${(x + 9)}^{2} = 14$ $(x+9)^2 = 14$
$x + 9 = \sqrt{14}$ $x + 9 = sqrt14$ or $x + 9 = - \sqrt{14}$ $x +9 = -sqrt14$

$x = \sqrt{14} - 9$ $color(green)(x = sqrt 14 -9$ or $x = - \sqrt{14} - 9$ $color(green)(x = -sqrt 14 -9$

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How do you solve the quadratic equation by completing the square: $x^{2} + 18 x + 67 = 0$ $x^2+18x+67=0$ ?

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How do you solve the quadratic equation by completing the square: x2+18x+67=0x^2+18x+67=0?

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How do you solve the quadratic equation by completing the square: $x^{2} + 18 x + 67 = 0$ $x^2+18x+67=0$ ?