8x^2+16x=5

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


Simplifying
8x2 + 16x = 5

Reorder the terms:
16x + 8x2 = 5

Solving
16x + 8x2 = 5

Solving for variable 'x'.

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

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

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

Divide each side by '8'.
-0.625 + 2x + x2 = 0

Move the constant term to the right:

Add '0.625' to each side of the equation.
-0.625 + 2x + 0.625 + x2 = 0 + 0.625

Reorder the terms:
-0.625 + 0.625 + 2x + x2 = 0 + 0.625

Combine like terms: -0.625 + 0.625 = 0.000
0.000 + 2x + x2 = 0 + 0.625
2x + x2 = 0 + 0.625

Combine like terms: 0 + 0.625 = 0.625
2x + x2 = 0.625

The x term is 2x.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2x + 1 + x2 = 0.625 + 1

Reorder the terms:
1 + 2x + x2 = 0.625 + 1

Combine like terms: 0.625 + 1 = 1.625
1 + 2x + x2 = 1.625

Factor a perfect square on the left side:
(x + 1)(x + 1) = 1.625

Calculate the square root of the right side: 1.274754878

Break this problem into two subproblems by setting 
(x + 1) equal to 1.274754878 and -1.274754878.

Subproblem 1

x + 1 = 1.274754878 Simplifying x + 1 = 1.274754878 Reorder the terms: 1 + x = 1.274754878 Solving 1 + x = 1.274754878 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 1.274754878 + -1 Combine like terms: 1 + -1 = 0 0 + x = 1.274754878 + -1 x = 1.274754878 + -1 Combine like terms: 1.274754878 + -1 = 0.274754878 x = 0.274754878 Simplifying x = 0.274754878

Subproblem 2

x + 1 = -1.274754878 Simplifying x + 1 = -1.274754878 Reorder the terms: 1 + x = -1.274754878 Solving 1 + x = -1.274754878 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -1.274754878 + -1 Combine like terms: 1 + -1 = 0 0 + x = -1.274754878 + -1 x = -1.274754878 + -1 Combine like terms: -1.274754878 + -1 = -2.274754878 x = -2.274754878 Simplifying x = -2.274754878

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.274754878, -2.274754878}

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