8x^2=x+5

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


Simplifying
8x2 = x + 5

Reorder the terms:
8x2 = 5 + x

Solving
8x2 = 5 + x

Solving for variable 'x'.

Reorder the terms:
-5 + -1x + 8x2 = 5 + x + -5 + -1x

Reorder the terms:
-5 + -1x + 8x2 = 5 + -5 + x + -1x

Combine like terms: 5 + -5 = 0
-5 + -1x + 8x2 = 0 + x + -1x
-5 + -1x + 8x2 = x + -1x

Combine like terms: x + -1x = 0
-5 + -1x + 8x2 = 0

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

Divide each side by '8'.
-0.625 + -0.125x + x2 = 0

Move the constant term to the right:

Add '0.625' to each side of the equation.
-0.625 + -0.125x + 0.625 + x2 = 0 + 0.625

Reorder the terms:
-0.625 + 0.625 + -0.125x + x2 = 0 + 0.625

Combine like terms: -0.625 + 0.625 = 0.000
0.000 + -0.125x + x2 = 0 + 0.625
-0.125x + x2 = 0 + 0.625

Combine like terms: 0 + 0.625 = 0.625
-0.125x + x2 = 0.625

The x term is -0.125x.  Take half its coefficient (-0.0625).
Square it (0.00390625) and add it to both sides.

Add '0.00390625' to each side of the equation.
-0.125x + 0.00390625 + x2 = 0.625 + 0.00390625

Reorder the terms:
0.00390625 + -0.125x + x2 = 0.625 + 0.00390625

Combine like terms: 0.625 + 0.00390625 = 0.62890625
0.00390625 + -0.125x + x2 = 0.62890625

Factor a perfect square on the left side:
(x + -0.0625)(x + -0.0625) = 0.62890625

Calculate the square root of the right side: 0.793036096

Break this problem into two subproblems by setting 
(x + -0.0625) equal to 0.793036096 and -0.793036096.

Subproblem 1

x + -0.0625 = 0.793036096 Simplifying x + -0.0625 = 0.793036096 Reorder the terms: -0.0625 + x = 0.793036096 Solving -0.0625 + x = 0.793036096 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.0625' to each side of the equation. -0.0625 + 0.0625 + x = 0.793036096 + 0.0625 Combine like terms: -0.0625 + 0.0625 = 0.0000 0.0000 + x = 0.793036096 + 0.0625 x = 0.793036096 + 0.0625 Combine like terms: 0.793036096 + 0.0625 = 0.855536096 x = 0.855536096 Simplifying x = 0.855536096

Subproblem 2

x + -0.0625 = -0.793036096 Simplifying x + -0.0625 = -0.793036096 Reorder the terms: -0.0625 + x = -0.793036096 Solving -0.0625 + x = -0.793036096 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.0625' to each side of the equation. -0.0625 + 0.0625 + x = -0.793036096 + 0.0625 Combine like terms: -0.0625 + 0.0625 = 0.0000 0.0000 + x = -0.793036096 + 0.0625 x = -0.793036096 + 0.0625 Combine like terms: -0.793036096 + 0.0625 = -0.730536096 x = -0.730536096 Simplifying x = -0.730536096

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.855536096, -0.730536096}

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