2x^2+27x-8.7=0

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Solution for 2x^2+27x-8.7=0 equation:


Simplifying
2x2 + 27x + -8.7 = 0

Reorder the terms:
-8.7 + 27x + 2x2 = 0

Solving
-8.7 + 27x + 2x2 = 0

Solving for variable 'x'.

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

Divide each side by '2'.
-4.35 + 13.5x + x2 = 0

Move the constant term to the right:

Add '4.35' to each side of the equation.
-4.35 + 13.5x + 4.35 + x2 = 0 + 4.35

Reorder the terms:
-4.35 + 4.35 + 13.5x + x2 = 0 + 4.35

Combine like terms: -4.35 + 4.35 = 0.00
0.00 + 13.5x + x2 = 0 + 4.35
13.5x + x2 = 0 + 4.35

Combine like terms: 0 + 4.35 = 4.35
13.5x + x2 = 4.35

The x term is 13.5x.  Take half its coefficient (6.75).
Square it (45.5625) and add it to both sides.

Add '45.5625' to each side of the equation.
13.5x + 45.5625 + x2 = 4.35 + 45.5625

Reorder the terms:
45.5625 + 13.5x + x2 = 4.35 + 45.5625

Combine like terms: 4.35 + 45.5625 = 49.9125
45.5625 + 13.5x + x2 = 49.9125

Factor a perfect square on the left side:
(x + 6.75)(x + 6.75) = 49.9125

Calculate the square root of the right side: 7.064877918

Break this problem into two subproblems by setting 
(x + 6.75) equal to 7.064877918 and -7.064877918.

Subproblem 1

x + 6.75 = 7.064877918 Simplifying x + 6.75 = 7.064877918 Reorder the terms: 6.75 + x = 7.064877918 Solving 6.75 + x = 7.064877918 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6.75' to each side of the equation. 6.75 + -6.75 + x = 7.064877918 + -6.75 Combine like terms: 6.75 + -6.75 = 0.00 0.00 + x = 7.064877918 + -6.75 x = 7.064877918 + -6.75 Combine like terms: 7.064877918 + -6.75 = 0.314877918 x = 0.314877918 Simplifying x = 0.314877918

Subproblem 2

x + 6.75 = -7.064877918 Simplifying x + 6.75 = -7.064877918 Reorder the terms: 6.75 + x = -7.064877918 Solving 6.75 + x = -7.064877918 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6.75' to each side of the equation. 6.75 + -6.75 + x = -7.064877918 + -6.75 Combine like terms: 6.75 + -6.75 = 0.00 0.00 + x = -7.064877918 + -6.75 x = -7.064877918 + -6.75 Combine like terms: -7.064877918 + -6.75 = -13.814877918 x = -13.814877918 Simplifying x = -13.814877918

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.314877918, -13.814877918}

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