7.9x^2+6.5x-8.7=0

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Solution for 7.9x^2+6.5x-8.7=0 equation:


Simplifying
7.9x2 + 6.5x + -8.7 = 0

Reorder the terms:
-8.7 + 6.5x + 7.9x2 = 0

Solving
-8.7 + 6.5x + 7.9x2 = 0

Solving for variable 'x'.

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

Divide each side by '7.9'.
-1.101265823 + 0.8227848101x + x2 = 0

Move the constant term to the right:

Add '1.101265823' to each side of the equation.
-1.101265823 + 0.8227848101x + 1.101265823 + x2 = 0 + 1.101265823

Reorder the terms:
-1.101265823 + 1.101265823 + 0.8227848101x + x2 = 0 + 1.101265823

Combine like terms: -1.101265823 + 1.101265823 = 0.000000000
0.000000000 + 0.8227848101x + x2 = 0 + 1.101265823
0.8227848101x + x2 = 0 + 1.101265823

Combine like terms: 0 + 1.101265823 = 1.101265823
0.8227848101x + x2 = 1.101265823

The x term is 0.8227848101x.  Take half its coefficient (0.4113924051).
Square it (0.1692437110) and add it to both sides.

Add '0.1692437110' to each side of the equation.
0.8227848101x + 0.1692437110 + x2 = 1.101265823 + 0.1692437110

Reorder the terms:
0.1692437110 + 0.8227848101x + x2 = 1.101265823 + 0.1692437110

Combine like terms: 1.101265823 + 0.1692437110 = 1.270509534
0.1692437110 + 0.8227848101x + x2 = 1.270509534

Factor a perfect square on the left side:
(x + 0.4113924051)(x + 0.4113924051) = 1.270509534

Calculate the square root of the right side: 1.127168813

Break this problem into two subproblems by setting 
(x + 0.4113924051) equal to 1.127168813 and -1.127168813.

Subproblem 1

x + 0.4113924051 = 1.127168813 Simplifying x + 0.4113924051 = 1.127168813 Reorder the terms: 0.4113924051 + x = 1.127168813 Solving 0.4113924051 + x = 1.127168813 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4113924051' to each side of the equation. 0.4113924051 + -0.4113924051 + x = 1.127168813 + -0.4113924051 Combine like terms: 0.4113924051 + -0.4113924051 = 0.0000000000 0.0000000000 + x = 1.127168813 + -0.4113924051 x = 1.127168813 + -0.4113924051 Combine like terms: 1.127168813 + -0.4113924051 = 0.7157764079 x = 0.7157764079 Simplifying x = 0.7157764079

Subproblem 2

x + 0.4113924051 = -1.127168813 Simplifying x + 0.4113924051 = -1.127168813 Reorder the terms: 0.4113924051 + x = -1.127168813 Solving 0.4113924051 + x = -1.127168813 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4113924051' to each side of the equation. 0.4113924051 + -0.4113924051 + x = -1.127168813 + -0.4113924051 Combine like terms: 0.4113924051 + -0.4113924051 = 0.0000000000 0.0000000000 + x = -1.127168813 + -0.4113924051 x = -1.127168813 + -0.4113924051 Combine like terms: -1.127168813 + -0.4113924051 = -1.5385612181 x = -1.5385612181 Simplifying x = -1.5385612181

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.7157764079, -1.5385612181}

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