How do you solve $x^{2} + 8 x = 14$ $x^2 + 8x = 14$ by completing the square?

Question

5903 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2015-04-29T10:36:33

$x^{2} + 8 x = 14$ $x^2 + 8x = 14$

To write the Left Hand Side as a Perfect Square, we add 16 to both sides

$x^{2} + 8 x + 16 = 14 + 16$ $x^2 + 8x + 16 = 14 + 16$

$x^{2} + 2 \cdot 4 \cdot x + 4^{2} = 30$ $x^2 + 2*4*x + 4^2 = 30$

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

${(x + 4)}^{2} = 30$ $(x+4)^2 = 30$

$x + 4 = \sqrt{30}$ $x + 4 = sqrt30$ or $x + 4 = - \sqrt{30}$ $x +4 = -sqrt30$

$x = \sqrt{30} - 4$ $color(green)(x = sqrt 30 - 4$ or $x = - \sqrt{30} + 4$ $color(green)(x = -sqrt 30 + 4$

How do you solve x^2 + 8x = 14x2+8x=14x^2 + 8x = 14 by completing the square?