Conplete the square to solve the quadratic equation. x[tex]1 {x}^{2} - 6x + 12 = 2x + 20[/tex]

Given the quadratic equation:

x^2 - 6x + 12 = 2x + 20

Complete the square and solve.

Solution:

In order to complete the square, we simply must transpose 2x and 20 to the other side of the equation, hence we must take note that when transposing a number, the sign changes.

= x^2 - 6x + 12 - 2x -20

= x^2 -8x - 8
a = 1

b = -8

c = -8

To solve for the value of x, we simply must look at the 2nd and 3rd value. First we must think of two numbers that when added, the answer is -8, and when multiplied, the answer is -8. Hence, if we are unable to find the number, we will use the quadratic formula.

The Quadratic formula:

x = −b ± √(b^2 − 4ac)/2a

is used to solve quadratic equations where a ≠ 0, in the form
ax^2+bx+c=0

When b^2−4ac=0 there is one real root.

When b^2−4ac>0 there are two real roots.

When b^2−4ac<0 there are no real roots, only a complex number

Substitute the given values of a, b and c to the quadratic formula.

x = −b ± √(b^2 − 4ac)/2a

x = −(-8) ± √((-8)^2 − 4(1)(-8))/2(1)

x = 8 ± √((64 + 32)/2

x = 8 ± √(96)/2

x = 8 ± 9.8/2

Solve for + - separately.

x = 8 + 9.8 /2

x = 17.8/2

x = 8.9

x = 8 - 9.8/2

x = -1.8/2

x = - 0.9

Final answer:

x = 8.9

x = - 0.9