8x^2+9=-55x

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Solution for 8x^2+9=-55x equation:


Simplifying
8x2 + 9 = -55x

Reorder the terms:
9 + 8x2 = -55x

Solving
9 + 8x2 = -55x

Solving for variable 'x'.

Reorder the terms:
9 + 55x + 8x2 = -55x + 55x

Combine like terms: -55x + 55x = 0
9 + 55x + 8x2 = 0

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

Divide each side by '8'.
1.125 + 6.875x + x2 = 0

Move the constant term to the right:

Add '-1.125' to each side of the equation.
1.125 + 6.875x + -1.125 + x2 = 0 + -1.125

Reorder the terms:
1.125 + -1.125 + 6.875x + x2 = 0 + -1.125

Combine like terms: 1.125 + -1.125 = 0.000
0.000 + 6.875x + x2 = 0 + -1.125
6.875x + x2 = 0 + -1.125

Combine like terms: 0 + -1.125 = -1.125
6.875x + x2 = -1.125

The x term is 6.875x.  Take half its coefficient (3.4375).
Square it (11.81640625) and add it to both sides.

Add '11.81640625' to each side of the equation.
6.875x + 11.81640625 + x2 = -1.125 + 11.81640625

Reorder the terms:
11.81640625 + 6.875x + x2 = -1.125 + 11.81640625

Combine like terms: -1.125 + 11.81640625 = 10.69140625
11.81640625 + 6.875x + x2 = 10.69140625

Factor a perfect square on the left side:
(x + 3.4375)(x + 3.4375) = 10.69140625

Calculate the square root of the right side: 3.26977159

Break this problem into two subproblems by setting 
(x + 3.4375) equal to 3.26977159 and -3.26977159.

Subproblem 1

x + 3.4375 = 3.26977159 Simplifying x + 3.4375 = 3.26977159 Reorder the terms: 3.4375 + x = 3.26977159 Solving 3.4375 + x = 3.26977159 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.4375' to each side of the equation. 3.4375 + -3.4375 + x = 3.26977159 + -3.4375 Combine like terms: 3.4375 + -3.4375 = 0.0000 0.0000 + x = 3.26977159 + -3.4375 x = 3.26977159 + -3.4375 Combine like terms: 3.26977159 + -3.4375 = -0.16772841 x = -0.16772841 Simplifying x = -0.16772841

Subproblem 2

x + 3.4375 = -3.26977159 Simplifying x + 3.4375 = -3.26977159 Reorder the terms: 3.4375 + x = -3.26977159 Solving 3.4375 + x = -3.26977159 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.4375' to each side of the equation. 3.4375 + -3.4375 + x = -3.26977159 + -3.4375 Combine like terms: 3.4375 + -3.4375 = 0.0000 0.0000 + x = -3.26977159 + -3.4375 x = -3.26977159 + -3.4375 Combine like terms: -3.26977159 + -3.4375 = -6.70727159 x = -6.70727159 Simplifying x = -6.70727159

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-0.16772841, -6.70727159}

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