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

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Answer 1 · 2016-05-28T17:06:53

The solutions are:
$color(green)(x = 3sqrt 3 - 5$ , $color(green)(x = -3sqrt 3 -5$

$x^2 +10x - 2 = 0$

$x^2 +10x = 2$

To write the Left Hand Side as a Perfect Square, we add 25 to both sides:

$x^2 +10x + color(blue)(25)= 2 + color(blue)(25)$

$x^2 + 2 * x * 5 + 5^2 = 27$

Using the Identity $color(blue)((a+b)^2 = a^2 + 2ab + b^2$ , we get

$(x+5)^2 = 27$

$x + 5 = sqrt27$ or $x +5 = -sqrt27$

(Note: prime factorising #27; 27 = 3 * 3 * 3 = 3^3

So, $sqrt27 = sqrt (3^3) = 3sqrt3$ )

$x + 5 = 3sqrt3$ or $x +5 = -3sqrt3$

$color(green)(x = 3sqrt 3 - 5$ , $color(green)(x = -3sqrt 3 -5$

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