(7.6-2x)(7.6-2x)=9.05(6.4+x)(x)

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Solution for (7.6-2x)(7.6-2x)=9.05(6.4+x)(x) equation: 


Simplifying
(7.6 + -2x)(7.6 + -2x) = 9.05(6.4 + x)(x)

Multiply (7.6 + -2x) * (7.6 + -2x)
(7.6(7.6 + -2x) + -2x * (7.6 + -2x)) = 9.05(6.4 + x)(x)
((7.6 * 7.6 + -2x * 7.6) + -2x * (7.6 + -2x)) = 9.05(6.4 + x)(x)
((57.76 + -15.2x) + -2x * (7.6 + -2x)) = 9.05(6.4 + x)(x)
(57.76 + -15.2x + (7.6 * -2x + -2x * -2x)) = 9.05(6.4 + x)(x)
(57.76 + -15.2x + (-15.2x + 4x2)) = 9.05(6.4 + x)(x)

Combine like terms: -15.2x + -15.2x = -30.4x
(57.76 + -30.4x + 4x2) = 9.05(6.4 + x)(x)

Reorder the terms for easier multiplication:
57.76 + -30.4x + 4x2 = 9.05x(6.4 + x)
57.76 + -30.4x + 4x2 = (6.4 * 9.05x + x * 9.05x)
57.76 + -30.4x + 4x2 = (57.92x + 9.05x2)

Solving
57.76 + -30.4x + 4x2 = 57.92x + 9.05x2

Solving for variable 'x'.

Reorder the terms:
57.76 + -30.4x + -57.92x + 4x2 + -9.05x2 = 57.92x + 9.05x2 + -57.92x + -9.05x2

Combine like terms: -30.4x + -57.92x = -88.32x
57.76 + -88.32x + 4x2 + -9.05x2 = 57.92x + 9.05x2 + -57.92x + -9.05x2

Combine like terms: 4x2 + -9.05x2 = -5.05x2
57.76 + -88.32x + -5.05x2 = 57.92x + 9.05x2 + -57.92x + -9.05x2

Reorder the terms:
57.76 + -88.32x + -5.05x2 = 57.92x + -57.92x + 9.05x2 + -9.05x2

Combine like terms: 57.92x + -57.92x = 0.00
57.76 + -88.32x + -5.05x2 = 0.00 + 9.05x2 + -9.05x2
57.76 + -88.32x + -5.05x2 = 9.05x2 + -9.05x2

Combine like terms: 9.05x2 + -9.05x2 = 0.00
57.76 + -88.32x + -5.05x2 = 0.00

Begin completing the square.  Divide all terms by
-5.05 the coefficient of the squared term: 

Divide each side by '-5.05'.
-11.43762376 + 17.48910891x + x2 = 0

Move the constant term to the right:

Add '11.43762376' to each side of the equation.
-11.43762376 + 17.48910891x + 11.43762376 + x2 = 0 + 11.43762376

Reorder the terms:
-11.43762376 + 11.43762376 + 17.48910891x + x2 = 0 + 11.43762376

Combine like terms: -11.43762376 + 11.43762376 = 0.00000000
0.00000000 + 17.48910891x + x2 = 0 + 11.43762376
17.48910891x + x2 = 0 + 11.43762376

Combine like terms: 0 + 11.43762376 = 11.43762376
17.48910891x + x2 = 11.43762376

The x term is 17.48910891x.  Take half its coefficient (8.744554455).
Square it (76.46723262) and add it to both sides.

Add '76.46723262' to each side of the equation.
17.48910891x + 76.46723262 + x2 = 11.43762376 + 76.46723262

Reorder the terms:
76.46723262 + 17.48910891x + x2 = 11.43762376 + 76.46723262

Combine like terms: 11.43762376 + 76.46723262 = 87.90485638
76.46723262 + 17.48910891x + x2 = 87.90485638

Factor a perfect square on the left side:
(x + 8.744554455)(x + 8.744554455) = 87.90485638

Calculate the square root of the right side: 9.375758976

Break this problem into two subproblems by setting 
(x + 8.744554455) equal to 9.375758976 and -9.375758976.


Subproblem 1
x + 8.744554455 = 9.375758976

Simplifying
x + 8.744554455 = 9.375758976

Reorder the terms:
8.744554455 + x = 9.375758976

Solving
8.744554455 + x = 9.375758976

Solving for variable 'x'.

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

Add '-8.744554455' to each side of the equation.
8.744554455 + -8.744554455 + x = 9.375758976 + -8.744554455

Combine like terms: 8.744554455 + -8.744554455 = 0.000000000
0.000000000 + x = 9.375758976 + -8.744554455
x = 9.375758976 + -8.744554455

Combine like terms: 9.375758976 + -8.744554455 = 0.631204521
x = 0.631204521

Simplifying
x = 0.631204521


Subproblem 2
x + 8.744554455 = -9.375758976

Simplifying
x + 8.744554455 = -9.375758976

Reorder the terms:
8.744554455 + x = -9.375758976

Solving
8.744554455 + x = -9.375758976

Solving for variable 'x'.

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

Add '-8.744554455' to each side of the equation.
8.744554455 + -8.744554455 + x = -9.375758976 + -8.744554455

Combine like terms: 8.744554455 + -8.744554455 = 0.000000000
0.000000000 + x = -9.375758976 + -8.744554455
x = -9.375758976 + -8.744554455

Combine like terms: -9.375758976 + -8.744554455 = -18.120313431
x = -18.120313431

Simplifying
x = -18.120313431


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.631204521, -18.120313431}

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