8x^2-2x=7

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Solution for 8x^2-2x=7 equation:


Simplifying
8x2 + -2x = 7

Reorder the terms:
-2x + 8x2 = 7

Solving
-2x + 8x2 = 7

Solving for variable 'x'.

Reorder the terms:
-7 + -2x + 8x2 = 7 + -7

Combine like terms: 7 + -7 = 0
-7 + -2x + 8x2 = 0

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

Divide each side by '8'.
-0.875 + -0.25x + x2 = 0

Move the constant term to the right:

Add '0.875' to each side of the equation.
-0.875 + -0.25x + 0.875 + x2 = 0 + 0.875

Reorder the terms:
-0.875 + 0.875 + -0.25x + x2 = 0 + 0.875

Combine like terms: -0.875 + 0.875 = 0.000
0.000 + -0.25x + x2 = 0 + 0.875
-0.25x + x2 = 0 + 0.875

Combine like terms: 0 + 0.875 = 0.875
-0.25x + x2 = 0.875

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 = 0.875 + 0.015625

Reorder the terms:
0.015625 + -0.25x + x2 = 0.875 + 0.015625

Combine like terms: 0.875 + 0.015625 = 0.890625
0.015625 + -0.25x + x2 = 0.890625

Factor a perfect square on the left side:
(x + -0.125)(x + -0.125) = 0.890625

Calculate the square root of the right side: 0.943729304

Break this problem into two subproblems by setting 
(x + -0.125) equal to 0.943729304 and -0.943729304.

Subproblem 1

x + -0.125 = 0.943729304 Simplifying x + -0.125 = 0.943729304 Reorder the terms: -0.125 + x = 0.943729304 Solving -0.125 + x = 0.943729304 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 = 0.943729304 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + x = 0.943729304 + 0.125 x = 0.943729304 + 0.125 Combine like terms: 0.943729304 + 0.125 = 1.068729304 x = 1.068729304 Simplifying x = 1.068729304

Subproblem 2

x + -0.125 = -0.943729304 Simplifying x + -0.125 = -0.943729304 Reorder the terms: -0.125 + x = -0.943729304 Solving -0.125 + x = -0.943729304 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 = -0.943729304 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + x = -0.943729304 + 0.125 x = -0.943729304 + 0.125 Combine like terms: -0.943729304 + 0.125 = -0.818729304 x = -0.818729304 Simplifying x = -0.818729304

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.068729304, -0.818729304}

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