How do you solve the quadratic equation by completing the square: $x^{2} + 8 x - 2 = 0$ $x^2+8x-2=0$ ?

Question

How do you solve the quadratic equation by completing the square: $x^{2} + 8 x - 2 = 0$ $x^2+8x-2=0$ ?

1 Answer

Impact of this question

1723 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2015-07-19T13:54:54

$x = \sqrt{18} - 4$ $color(green)(x = sqrt 18 - 4$ or $x = - \sqrt{18} - 4$ $color(green)(x = -sqrt 18 -4$

Explanation:

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

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

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

$x^{2} + 2 \cdot 4 \cdot x + 4^{2} = 18$ $x^2 + 2*4*x + 4^2 = 18$

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
${(x + 4)}^{2} = 18$ $(x+4)^2 = 18$
$x + 4 = \sqrt{18}$ $x + 4 = sqrt18$ or $x + 4 = - \sqrt{18}$ $x +4 = -sqrt18$
$x = \sqrt{18} - 4$ $color(green)(x = sqrt 18 - 4$ or $x = - \sqrt{18} - 4$ $color(green)(x = -sqrt 18 -4$

Science

Math

Humanities

... and beyond

How do you solve the quadratic equation by completing the square: $x^{2} + 8 x - 2 = 0$ $x^2+8x-2=0$ ?

1 Answer

Explanation:

Related questions

Impact of this question

Science

Math

Humanities

... and beyond

How do you solve the quadratic equation by completing the square: x2+8x−2=0x^2+8x-2=0?

1 Answer

Explanation:

Related questions

Impact of this question

How do you solve the quadratic equation by completing the square: $x^{2} + 8 x - 2 = 0$ $x^2+8x-2=0$ ?