Question

Solve x2 − 12x + 5 = 0 using the completing-the-square method. x = six plus or minus the square root of five x = negative six plus or minus the square root of five x = six plus or minus the square root of thirty one x = negative six plus or minus the square root of thirty one

Answer 1

we are given

$x^2-12x+5=0$

we have to solve it by completing square method

step-1: Move 5 on right side

$x^2-12x+5-5=0-5$

$x^2-12x=-5$

step-2: Break middle term

$x^2-2*6*x=-5$

step-3: Add 6^2 both sides

$x^2-2*6*x+(6)^2=-5+(6)^2$

$(x-6)^2=31$

step-3: Solve for x

$\sqrt{(x-6)^2} =\sqrt{31}$

we wil get two values

First value is

$x-6=\sqrt{31}$

add both sides 6

$x-6+6=6+\sqrt{31}$

$x=6+\sqrt{31}$

Second value is

$x-6=-\sqrt{31}$

add both sides 6

$x-6+6=6-\sqrt{31}$

$x=6-\sqrt{31}$

so, solutions are

$x=6+\sqrt{31}$

$x=6-\sqrt{31}$.............Answer