8x^2-2x-18=15

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Solution for 8x^2-2x-18=15 equation:


Simplifying
8x2 + -2x + -18 = 15

Reorder the terms:
-18 + -2x + 8x2 = 15

Solving
-18 + -2x + 8x2 = 15

Solving for variable 'x'.

Reorder the terms:
-18 + -15 + -2x + 8x2 = 15 + -15

Combine like terms: -18 + -15 = -33
-33 + -2x + 8x2 = 15 + -15

Combine like terms: 15 + -15 = 0
-33 + -2x + 8x2 = 0

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

Divide each side by '8'.
-4.125 + -0.25x + x2 = 0

Move the constant term to the right:

Add '4.125' to each side of the equation.
-4.125 + -0.25x + 4.125 + x2 = 0 + 4.125

Reorder the terms:
-4.125 + 4.125 + -0.25x + x2 = 0 + 4.125

Combine like terms: -4.125 + 4.125 = 0.000
0.000 + -0.25x + x2 = 0 + 4.125
-0.25x + x2 = 0 + 4.125

Combine like terms: 0 + 4.125 = 4.125
-0.25x + x2 = 4.125

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 = 4.125 + 0.015625

Reorder the terms:
0.015625 + -0.25x + x2 = 4.125 + 0.015625

Combine like terms: 4.125 + 0.015625 = 4.140625
0.015625 + -0.25x + x2 = 4.140625

Factor a perfect square on the left side:
(x + -0.125)(x + -0.125) = 4.140625

Calculate the square root of the right side: 2.034852575

Break this problem into two subproblems by setting 
(x + -0.125) equal to 2.034852575 and -2.034852575.

Subproblem 1

x + -0.125 = 2.034852575 Simplifying x + -0.125 = 2.034852575 Reorder the terms: -0.125 + x = 2.034852575 Solving -0.125 + x = 2.034852575 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 = 2.034852575 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + x = 2.034852575 + 0.125 x = 2.034852575 + 0.125 Combine like terms: 2.034852575 + 0.125 = 2.159852575 x = 2.159852575 Simplifying x = 2.159852575

Subproblem 2

x + -0.125 = -2.034852575 Simplifying x + -0.125 = -2.034852575 Reorder the terms: -0.125 + x = -2.034852575 Solving -0.125 + x = -2.034852575 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 = -2.034852575 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + x = -2.034852575 + 0.125 x = -2.034852575 + 0.125 Combine like terms: -2.034852575 + 0.125 = -1.909852575 x = -1.909852575 Simplifying x = -1.909852575

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.159852575, -1.909852575}

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