(2x)(2x)=x+20

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Solution for (2x)(2x)=x+20 equation:


Simplifying
(2x)(2x) = x + 20

Remove parenthesis around (2x)
2x(2x) = x + 20

Remove parenthesis around (2x)
2x * 2x = x + 20

Reorder the terms for easier multiplication:
2 * 2x * x = x + 20

Multiply 2 * 2
4x * x = x + 20

Multiply x * x
4x2 = x + 20

Reorder the terms:
4x2 = 20 + x

Solving
4x2 = 20 + x

Solving for variable 'x'.

Reorder the terms:
-20 + -1x + 4x2 = 20 + x + -20 + -1x

Reorder the terms:
-20 + -1x + 4x2 = 20 + -20 + x + -1x

Combine like terms: 20 + -20 = 0
-20 + -1x + 4x2 = 0 + x + -1x
-20 + -1x + 4x2 = x + -1x

Combine like terms: x + -1x = 0
-20 + -1x + 4x2 = 0

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

Divide each side by '4'.
-5 + -0.25x + x2 = 0

Move the constant term to the right:

Add '5' to each side of the equation.
-5 + -0.25x + 5 + x2 = 0 + 5

Reorder the terms:
-5 + 5 + -0.25x + x2 = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -0.25x + x2 = 0 + 5
-0.25x + x2 = 0 + 5

Combine like terms: 0 + 5 = 5
-0.25x + x2 = 5

The x term is -0.25x.  Take half its coefficient (-0.125).
Square it (0.015625) and add it to both sides.

Add '0.015625' to each side of the equation.
-0.25x + 0.015625 + x2 = 5 + 0.015625

Reorder the terms:
0.015625 + -0.25x + x2 = 5 + 0.015625

Combine like terms: 5 + 0.015625 = 5.015625
0.015625 + -0.25x + x2 = 5.015625

Factor a perfect square on the left side:
(x + -0.125)(x + -0.125) = 5.015625

Calculate the square root of the right side: 2.239559108

Break this problem into two subproblems by setting 
(x + -0.125) equal to 2.239559108 and -2.239559108.

Subproblem 1

x + -0.125 = 2.239559108 Simplifying x + -0.125 = 2.239559108 Reorder the terms: -0.125 + x = 2.239559108 Solving -0.125 + x = 2.239559108 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.125' to each side of the equation. -0.125 + 0.125 + x = 2.239559108 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + x = 2.239559108 + 0.125 x = 2.239559108 + 0.125 Combine like terms: 2.239559108 + 0.125 = 2.364559108 x = 2.364559108 Simplifying x = 2.364559108

Subproblem 2

x + -0.125 = -2.239559108 Simplifying x + -0.125 = -2.239559108 Reorder the terms: -0.125 + x = -2.239559108 Solving -0.125 + x = -2.239559108 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.125' to each side of the equation. -0.125 + 0.125 + x = -2.239559108 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + x = -2.239559108 + 0.125 x = -2.239559108 + 0.125 Combine like terms: -2.239559108 + 0.125 = -2.114559108 x = -2.114559108 Simplifying x = -2.114559108

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.364559108, -2.114559108}

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