How do you solve using the completing the square method $x^{2} - 10 x - 4 = 0$ $x^2-10x-4=0$ ?

Question

1621 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-02-26T13:29:04

$x = 5 \pm \sqrt{2}$ $x = 5 +-sqrt2$

$x^{2} - 10 x - 4 = 0$ $x^2 - 10x - 4 = 0$

Notice 10x

This can be our $2 a b$ $2ab$ term

${(a - b)}^{2} = a^{2} - 2 a b + b^{2}$ $(a-b)^ 2 = a^2 -2ab + b^2$

-2ab = -10x

ab =5x
We have a = x

b = 5

$x^{2} - 10 x + 5^{2} - 5^{2} - 4 = 0$ $x^2 - 10x + 5^2 - 5^2- 4 = 0$

${(x - 5)}^{2} = 4 + 25 = 29$ $(x-5)^2 = 4 + 25 = 29$

$x - 5 = \pm \sqrt{2}$ $x - 5 = +-sqrt2$

$x = 5 \pm \sqrt{2}$ $x = 5 +-sqrt2$

How do you solve using the completing the square method x2−10x−4=0x^2-10x-4=0?