4x^2-11=(x+8)(x+8)

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Solution for 4x^2-11=(x+8)(x+8) equation: 


Simplifying
4x2 + -11 = (x + 8)(x + 8)

Reorder the terms:
-11 + 4x2 = (x + 8)(x + 8)

Reorder the terms:
-11 + 4x2 = (8 + x)(x + 8)

Reorder the terms:
-11 + 4x2 = (8 + x)(8 + x)

Multiply (8 + x) * (8 + x)
-11 + 4x2 = (8(8 + x) + x(8 + x))
-11 + 4x2 = ((8 * 8 + x * 8) + x(8 + x))
-11 + 4x2 = ((64 + 8x) + x(8 + x))
-11 + 4x2 = (64 + 8x + (8 * x + x * x))
-11 + 4x2 = (64 + 8x + (8x + x2))

Combine like terms: 8x + 8x = 16x
-11 + 4x2 = (64 + 16x + x2)

Solving
-11 + 4x2 = 64 + 16x + x2

Solving for variable 'x'.

Reorder the terms:
-11 + -64 + -16x + 4x2 + -1x2 = 64 + 16x + x2 + -64 + -16x + -1x2

Combine like terms: -11 + -64 = -75
-75 + -16x + 4x2 + -1x2 = 64 + 16x + x2 + -64 + -16x + -1x2

Combine like terms: 4x2 + -1x2 = 3x2
-75 + -16x + 3x2 = 64 + 16x + x2 + -64 + -16x + -1x2

Reorder the terms:
-75 + -16x + 3x2 = 64 + -64 + 16x + -16x + x2 + -1x2

Combine like terms: 64 + -64 = 0
-75 + -16x + 3x2 = 0 + 16x + -16x + x2 + -1x2
-75 + -16x + 3x2 = 16x + -16x + x2 + -1x2

Combine like terms: 16x + -16x = 0
-75 + -16x + 3x2 = 0 + x2 + -1x2
-75 + -16x + 3x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-75 + -16x + 3x2 = 0

Factor a trinomial.
(-3 + -1x)(25 + -3x) = 0


Subproblem 1
Set the factor '(-3 + -1x)' equal to zero and attempt to solve:

Simplifying
-3 + -1x = 0

Solving
-3 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '3' to each side of the equation.
-3 + 3 + -1x = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1x = 0 + 3
-1x = 0 + 3

Combine like terms: 0 + 3 = 3
-1x = 3

Divide each side by '-1'.
x = -3

Simplifying
x = -3

Subproblem 2
Set the factor '(25 + -3x)' equal to zero and attempt to solve:

Simplifying
25 + -3x = 0

Solving
25 + -3x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-25' to each side of the equation.
25 + -25 + -3x = 0 + -25

Combine like terms: 25 + -25 = 0
0 + -3x = 0 + -25
-3x = 0 + -25

Combine like terms: 0 + -25 = -25
-3x = -25

Divide each side by '-3'.
x = 8.333333333

Simplifying
x = 8.333333333
Solution
x = {-3, 8.333333333}

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