8x^2=18+5x

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Solution for 8x^2=18+5x equation:


Simplifying
8x2 = 18 + 5x

Solving
8x2 = 18 + 5x

Solving for variable 'x'.

Reorder the terms:
-18 + -5x + 8x2 = 18 + 5x + -18 + -5x

Reorder the terms:
-18 + -5x + 8x2 = 18 + -18 + 5x + -5x

Combine like terms: 18 + -18 = 0
-18 + -5x + 8x2 = 0 + 5x + -5x
-18 + -5x + 8x2 = 5x + -5x

Combine like terms: 5x + -5x = 0
-18 + -5x + 8x2 = 0

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

Divide each side by '8'.
-2.25 + -0.625x + x2 = 0

Move the constant term to the right:

Add '2.25' to each side of the equation.
-2.25 + -0.625x + 2.25 + x2 = 0 + 2.25

Reorder the terms:
-2.25 + 2.25 + -0.625x + x2 = 0 + 2.25

Combine like terms: -2.25 + 2.25 = 0.00
0.00 + -0.625x + x2 = 0 + 2.25
-0.625x + x2 = 0 + 2.25

Combine like terms: 0 + 2.25 = 2.25
-0.625x + x2 = 2.25

The x term is -0.625x.  Take half its coefficient (-0.3125).
Square it (0.09765625) and add it to both sides.

Add '0.09765625' to each side of the equation.
-0.625x + 0.09765625 + x2 = 2.25 + 0.09765625

Reorder the terms:
0.09765625 + -0.625x + x2 = 2.25 + 0.09765625

Combine like terms: 2.25 + 0.09765625 = 2.34765625
0.09765625 + -0.625x + x2 = 2.34765625

Factor a perfect square on the left side:
(x + -0.3125)(x + -0.3125) = 2.34765625

Calculate the square root of the right side: 1.532206334

Break this problem into two subproblems by setting 
(x + -0.3125) equal to 1.532206334 and -1.532206334.

Subproblem 1

x + -0.3125 = 1.532206334 Simplifying x + -0.3125 = 1.532206334 Reorder the terms: -0.3125 + x = 1.532206334 Solving -0.3125 + x = 1.532206334 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3125' to each side of the equation. -0.3125 + 0.3125 + x = 1.532206334 + 0.3125 Combine like terms: -0.3125 + 0.3125 = 0.0000 0.0000 + x = 1.532206334 + 0.3125 x = 1.532206334 + 0.3125 Combine like terms: 1.532206334 + 0.3125 = 1.844706334 x = 1.844706334 Simplifying x = 1.844706334

Subproblem 2

x + -0.3125 = -1.532206334 Simplifying x + -0.3125 = -1.532206334 Reorder the terms: -0.3125 + x = -1.532206334 Solving -0.3125 + x = -1.532206334 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3125' to each side of the equation. -0.3125 + 0.3125 + x = -1.532206334 + 0.3125 Combine like terms: -0.3125 + 0.3125 = 0.0000 0.0000 + x = -1.532206334 + 0.3125 x = -1.532206334 + 0.3125 Combine like terms: -1.532206334 + 0.3125 = -1.219706334 x = -1.219706334 Simplifying x = -1.219706334

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.844706334, -1.219706334}

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