Solve by factoring x^2-4x-8=8 Show your work

Given the numerical equation:

x^2 - 4x - 8 = 8

Solve by factoring.

Solution:

In order to solve the given numerical equation, the first step is to transpose 8 on the other side of the equation, hence it must be taken to note  that in transposing a number, the sign changes.

x^2 - 4x - 8 = 8

x^2 - 4x - 8 - 8 = 0

x^2 - 4x - 16 = 0

a = 1

b = -4

c = -16

In order to solvethe factors of the equation, we simply must look at the 2nd and 3rd value. First we must think of two numbers that when added, the answer is -4, and when multiplied, the answer is -16. 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 = −(-4) ± √((-4)^2 − 4(1)(-16)))/2(1)
x =4 ± √(16 + 64))/2
x =4 ± √(80)/2
x =4 ± 8.94/2

Solve for + - separately.

x = 4 + 8.94/2
x = 12.94/2
x = 6.47

x = 4 - 8.94/2
x = -4.94/
x = -2.47

( x - 6.47)( x + 2.47 )

Final answer:

( x - 6.47)( x + 2.47 )