8x^2-9=-3x

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Solution for 8x^2-9=-3x equation:


Simplifying
8x2 + -9 = -3x

Reorder the terms:
-9 + 8x2 = -3x

Solving
-9 + 8x2 = -3x

Solving for variable 'x'.

Reorder the terms:
-9 + 3x + 8x2 = -3x + 3x

Combine like terms: -3x + 3x = 0
-9 + 3x + 8x2 = 0

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

Divide each side by '8'.
-1.125 + 0.375x + x2 = 0

Move the constant term to the right:

Add '1.125' to each side of the equation.
-1.125 + 0.375x + 1.125 + x2 = 0 + 1.125

Reorder the terms:
-1.125 + 1.125 + 0.375x + x2 = 0 + 1.125

Combine like terms: -1.125 + 1.125 = 0.000
0.000 + 0.375x + x2 = 0 + 1.125
0.375x + x2 = 0 + 1.125

Combine like terms: 0 + 1.125 = 1.125
0.375x + x2 = 1.125

The x term is 0.375x.  Take half its coefficient (0.1875).
Square it (0.03515625) and add it to both sides.

Add '0.03515625' to each side of the equation.
0.375x + 0.03515625 + x2 = 1.125 + 0.03515625

Reorder the terms:
0.03515625 + 0.375x + x2 = 1.125 + 0.03515625

Combine like terms: 1.125 + 0.03515625 = 1.16015625
0.03515625 + 0.375x + x2 = 1.16015625

Factor a perfect square on the left side:
(x + 0.1875)(x + 0.1875) = 1.16015625

Calculate the square root of the right side: 1.077105496

Break this problem into two subproblems by setting 
(x + 0.1875) equal to 1.077105496 and -1.077105496.

Subproblem 1

x + 0.1875 = 1.077105496 Simplifying x + 0.1875 = 1.077105496 Reorder the terms: 0.1875 + x = 1.077105496 Solving 0.1875 + x = 1.077105496 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1875' to each side of the equation. 0.1875 + -0.1875 + x = 1.077105496 + -0.1875 Combine like terms: 0.1875 + -0.1875 = 0.0000 0.0000 + x = 1.077105496 + -0.1875 x = 1.077105496 + -0.1875 Combine like terms: 1.077105496 + -0.1875 = 0.889605496 x = 0.889605496 Simplifying x = 0.889605496

Subproblem 2

x + 0.1875 = -1.077105496 Simplifying x + 0.1875 = -1.077105496 Reorder the terms: 0.1875 + x = -1.077105496 Solving 0.1875 + x = -1.077105496 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1875' to each side of the equation. 0.1875 + -0.1875 + x = -1.077105496 + -0.1875 Combine like terms: 0.1875 + -0.1875 = 0.0000 0.0000 + x = -1.077105496 + -0.1875 x = -1.077105496 + -0.1875 Combine like terms: -1.077105496 + -0.1875 = -1.264605496 x = -1.264605496 Simplifying x = -1.264605496

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.889605496, -1.264605496}

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