4x=16x^2+8x-5

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Solution for 4x=16x^2+8x-5 equation:


Simplifying
4x = 16x2 + 8x + -5

Reorder the terms:
4x = -5 + 8x + 16x2

Solving
4x = -5 + 8x + 16x2

Solving for variable 'x'.

Reorder the terms:
5 + 4x + -8x + -16x2 = -5 + 8x + 16x2 + 5 + -8x + -16x2

Combine like terms: 4x + -8x = -4x
5 + -4x + -16x2 = -5 + 8x + 16x2 + 5 + -8x + -16x2

Reorder the terms:
5 + -4x + -16x2 = -5 + 5 + 8x + -8x + 16x2 + -16x2

Combine like terms: -5 + 5 = 0
5 + -4x + -16x2 = 0 + 8x + -8x + 16x2 + -16x2
5 + -4x + -16x2 = 8x + -8x + 16x2 + -16x2

Combine like terms: 8x + -8x = 0
5 + -4x + -16x2 = 0 + 16x2 + -16x2
5 + -4x + -16x2 = 16x2 + -16x2

Combine like terms: 16x2 + -16x2 = 0
5 + -4x + -16x2 = 0

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

Divide each side by '-16'.
-0.3125 + 0.25x + x2 = 0

Move the constant term to the right:

Add '0.3125' to each side of the equation.
-0.3125 + 0.25x + 0.3125 + x2 = 0 + 0.3125

Reorder the terms:
-0.3125 + 0.3125 + 0.25x + x2 = 0 + 0.3125

Combine like terms: -0.3125 + 0.3125 = 0.0000
0.0000 + 0.25x + x2 = 0 + 0.3125
0.25x + x2 = 0 + 0.3125

Combine like terms: 0 + 0.3125 = 0.3125
0.25x + x2 = 0.3125

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 = 0.3125 + 0.015625

Reorder the terms:
0.015625 + 0.25x + x2 = 0.3125 + 0.015625

Combine like terms: 0.3125 + 0.015625 = 0.328125
0.015625 + 0.25x + x2 = 0.328125

Factor a perfect square on the left side:
(x + 0.125)(x + 0.125) = 0.328125

Calculate the square root of the right side: 0.572821962

Break this problem into two subproblems by setting 
(x + 0.125) equal to 0.572821962 and -0.572821962.

Subproblem 1

x + 0.125 = 0.572821962 Simplifying x + 0.125 = 0.572821962 Reorder the terms: 0.125 + x = 0.572821962 Solving 0.125 + x = 0.572821962 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 = 0.572821962 + -0.125 Combine like terms: 0.125 + -0.125 = 0.000 0.000 + x = 0.572821962 + -0.125 x = 0.572821962 + -0.125 Combine like terms: 0.572821962 + -0.125 = 0.447821962 x = 0.447821962 Simplifying x = 0.447821962

Subproblem 2

x + 0.125 = -0.572821962 Simplifying x + 0.125 = -0.572821962 Reorder the terms: 0.125 + x = -0.572821962 Solving 0.125 + x = -0.572821962 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 = -0.572821962 + -0.125 Combine like terms: 0.125 + -0.125 = 0.000 0.000 + x = -0.572821962 + -0.125 x = -0.572821962 + -0.125 Combine like terms: -0.572821962 + -0.125 = -0.697821962 x = -0.697821962 Simplifying x = -0.697821962

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.447821962, -0.697821962}

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