5=4(x-9)(x-9)

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Solution for 5=4(x-9)(x-9) equation:


Simplifying
5 = 4(x + -9)(x + -9)

Reorder the terms:
5 = 4(-9 + x)(x + -9)

Reorder the terms:
5 = 4(-9 + x)(-9 + x)

Multiply (-9 + x) * (-9 + x)
5 = 4(-9(-9 + x) + x(-9 + x))
5 = 4((-9 * -9 + x * -9) + x(-9 + x))
5 = 4((81 + -9x) + x(-9 + x))
5 = 4(81 + -9x + (-9 * x + x * x))
5 = 4(81 + -9x + (-9x + x2))

Combine like terms: -9x + -9x = -18x
5 = 4(81 + -18x + x2)
5 = (81 * 4 + -18x * 4 + x2 * 4)
5 = (324 + -72x + 4x2)

Solving
5 = 324 + -72x + 4x2

Solving for variable 'x'.

Combine like terms: 5 + -324 = -319
-319 + 72x + -4x2 = 324 + -72x + 4x2 + -324 + 72x + -4x2

Reorder the terms:
-319 + 72x + -4x2 = 324 + -324 + -72x + 72x + 4x2 + -4x2

Combine like terms: 324 + -324 = 0
-319 + 72x + -4x2 = 0 + -72x + 72x + 4x2 + -4x2
-319 + 72x + -4x2 = -72x + 72x + 4x2 + -4x2

Combine like terms: -72x + 72x = 0
-319 + 72x + -4x2 = 0 + 4x2 + -4x2
-319 + 72x + -4x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
-319 + 72x + -4x2 = 0

Begin completing the square.  Divide all terms by
-4 the coefficient of the squared term: 

Divide each side by '-4'.
79.75 + -18x + x2 = 0

Move the constant term to the right:

Add '-79.75' to each side of the equation.
79.75 + -18x + -79.75 + x2 = 0 + -79.75

Reorder the terms:
79.75 + -79.75 + -18x + x2 = 0 + -79.75

Combine like terms: 79.75 + -79.75 = 0.00
0.00 + -18x + x2 = 0 + -79.75
-18x + x2 = 0 + -79.75

Combine like terms: 0 + -79.75 = -79.75
-18x + x2 = -79.75

The x term is -18x.  Take half its coefficient (-9).
Square it (81) and add it to both sides.

Add '81' to each side of the equation.
-18x + 81 + x2 = -79.75 + 81

Reorder the terms:
81 + -18x + x2 = -79.75 + 81

Combine like terms: -79.75 + 81 = 1.25
81 + -18x + x2 = 1.25

Factor a perfect square on the left side:
(x + -9)(x + -9) = 1.25

Calculate the square root of the right side: 1.118033989

Break this problem into two subproblems by setting 
(x + -9) equal to 1.118033989 and -1.118033989.

Subproblem 1

x + -9 = 1.118033989 Simplifying x + -9 = 1.118033989 Reorder the terms: -9 + x = 1.118033989 Solving -9 + x = 1.118033989 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + x = 1.118033989 + 9 Combine like terms: -9 + 9 = 0 0 + x = 1.118033989 + 9 x = 1.118033989 + 9 Combine like terms: 1.118033989 + 9 = 10.118033989 x = 10.118033989 Simplifying x = 10.118033989

Subproblem 2

x + -9 = -1.118033989 Simplifying x + -9 = -1.118033989 Reorder the terms: -9 + x = -1.118033989 Solving -9 + x = -1.118033989 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + x = -1.118033989 + 9 Combine like terms: -9 + 9 = 0 0 + x = -1.118033989 + 9 x = -1.118033989 + 9 Combine like terms: -1.118033989 + 9 = 7.881966011 x = 7.881966011 Simplifying x = 7.881966011

Solution

The solution to the problem is based on the solutions from the subproblems. x = {10.118033989, 7.881966011}

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