4x*4x=8x+5

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Solution for 4x*4x=8x+5 equation:


Simplifying
4x * 4x = 8x + 5

Reorder the terms for easier multiplication:
4 * 4x * x = 8x + 5

Multiply 4 * 4
16x * x = 8x + 5

Multiply x * x
16x2 = 8x + 5

Reorder the terms:
16x2 = 5 + 8x

Solving
16x2 = 5 + 8x

Solving for variable 'x'.

Reorder the terms:
-5 + -8x + 16x2 = 5 + 8x + -5 + -8x

Reorder the terms:
-5 + -8x + 16x2 = 5 + -5 + 8x + -8x

Combine like terms: 5 + -5 = 0
-5 + -8x + 16x2 = 0 + 8x + -8x
-5 + -8x + 16x2 = 8x + -8x

Combine like terms: 8x + -8x = 0
-5 + -8x + 16x2 = 0

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

Divide each side by '16'.
-0.3125 + -0.5x + x2 = 0

Move the constant term to the right:

Add '0.3125' to each side of the equation.
-0.3125 + -0.5x + 0.3125 + x2 = 0 + 0.3125

Reorder the terms:
-0.3125 + 0.3125 + -0.5x + x2 = 0 + 0.3125

Combine like terms: -0.3125 + 0.3125 = 0.0000
0.0000 + -0.5x + x2 = 0 + 0.3125
-0.5x + x2 = 0 + 0.3125

Combine like terms: 0 + 0.3125 = 0.3125
-0.5x + x2 = 0.3125

The x term is -0.5x.  Take half its coefficient (-0.25).
Square it (0.0625) and add it to both sides.

Add '0.0625' to each side of the equation.
-0.5x + 0.0625 + x2 = 0.3125 + 0.0625

Reorder the terms:
0.0625 + -0.5x + x2 = 0.3125 + 0.0625

Combine like terms: 0.3125 + 0.0625 = 0.375
0.0625 + -0.5x + x2 = 0.375

Factor a perfect square on the left side:
(x + -0.25)(x + -0.25) = 0.375

Calculate the square root of the right side: 0.612372436

Break this problem into two subproblems by setting 
(x + -0.25) equal to 0.612372436 and -0.612372436.

Subproblem 1

x + -0.25 = 0.612372436 Simplifying x + -0.25 = 0.612372436 Reorder the terms: -0.25 + x = 0.612372436 Solving -0.25 + x = 0.612372436 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + x = 0.612372436 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = 0.612372436 + 0.25 x = 0.612372436 + 0.25 Combine like terms: 0.612372436 + 0.25 = 0.862372436 x = 0.862372436 Simplifying x = 0.862372436

Subproblem 2

x + -0.25 = -0.612372436 Simplifying x + -0.25 = -0.612372436 Reorder the terms: -0.25 + x = -0.612372436 Solving -0.25 + x = -0.612372436 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + x = -0.612372436 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = -0.612372436 + 0.25 x = -0.612372436 + 0.25 Combine like terms: -0.612372436 + 0.25 = -0.362372436 x = -0.362372436 Simplifying x = -0.362372436

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.862372436, -0.362372436}

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