Question

Solve the equation by completing the square. Round to the nearest hundredth if necessary. x2 – 4x = 5

Answer 1

Solve for x over the real numbers:
x^2 - 4 x = 5

Subtract 5 from both sides:
x^2 - 4 x - 5 = 0

x = (4 ± sqrt((-4)^2 - 4 (-5)))/2 = (4 ± sqrt(16 + 20))/2 = (4 ± sqrt(36))/2:
x = (4 + sqrt(36))/2 or x = (4 - sqrt(36))/2

sqrt(36) = sqrt(4×9) = sqrt(2^2×3^2) = 2×3 = 6:
x = (4 + 6)/2 or x = (4 - 6)/2

(4 + 6)/2 = 10/2 = 5:
x = 5 or x = (4 - 6)/2

(4 - 6)/2 = -2/2 = -1:

Answer: x = 5 or x = -1

Answer 2

x = 5 or x = -1

Explanation:

x^2 – 4x = 5

Solve it by completing the square method

In completing the square method, we take the coefficient of x that is -4, divide it by 2 and then square it

-4/2 = -2

square it (-2)^2 = 4

Now add 4 on both sides

x^2 – 4x +4 = 5+4

x^2 – 4x +4 = 9

Now factor the left hand side

(x-2)(x-2)=9

(x-2)^2 = 9

Take square root on both sides

x-2 = +-3

x-2 = 3 , so x= 5

x-2 = -3, so x= -1