8x^2+59x+40=0

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Solution for 8x^2+59x+40=0 equation:


Simplifying
8x2 + 59x + 40 = 0

Reorder the terms:
40 + 59x + 8x2 = 0

Solving
40 + 59x + 8x2 = 0

Solving for variable 'x'.

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

Divide each side by '8'.
5 + 7.375x + x2 = 0

Move the constant term to the right:

Add '-5' to each side of the equation.
5 + 7.375x + -5 + x2 = 0 + -5

Reorder the terms:
5 + -5 + 7.375x + x2 = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 7.375x + x2 = 0 + -5
7.375x + x2 = 0 + -5

Combine like terms: 0 + -5 = -5
7.375x + x2 = -5

The x term is 7.375x.  Take half its coefficient (3.6875).
Square it (13.59765625) and add it to both sides.

Add '13.59765625' to each side of the equation.
7.375x + 13.59765625 + x2 = -5 + 13.59765625

Reorder the terms:
13.59765625 + 7.375x + x2 = -5 + 13.59765625

Combine like terms: -5 + 13.59765625 = 8.59765625
13.59765625 + 7.375x + x2 = 8.59765625

Factor a perfect square on the left side:
(x + 3.6875)(x + 3.6875) = 8.59765625

Calculate the square root of the right side: 2.932176026

Break this problem into two subproblems by setting 
(x + 3.6875) equal to 2.932176026 and -2.932176026.

Subproblem 1

x + 3.6875 = 2.932176026 Simplifying x + 3.6875 = 2.932176026 Reorder the terms: 3.6875 + x = 2.932176026 Solving 3.6875 + x = 2.932176026 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.6875' to each side of the equation. 3.6875 + -3.6875 + x = 2.932176026 + -3.6875 Combine like terms: 3.6875 + -3.6875 = 0.0000 0.0000 + x = 2.932176026 + -3.6875 x = 2.932176026 + -3.6875 Combine like terms: 2.932176026 + -3.6875 = -0.755323974 x = -0.755323974 Simplifying x = -0.755323974

Subproblem 2

x + 3.6875 = -2.932176026 Simplifying x + 3.6875 = -2.932176026 Reorder the terms: 3.6875 + x = -2.932176026 Solving 3.6875 + x = -2.932176026 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.6875' to each side of the equation. 3.6875 + -3.6875 + x = -2.932176026 + -3.6875 Combine like terms: 3.6875 + -3.6875 = 0.0000 0.0000 + x = -2.932176026 + -3.6875 x = -2.932176026 + -3.6875 Combine like terms: -2.932176026 + -3.6875 = -6.619676026 x = -6.619676026 Simplifying x = -6.619676026

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-0.755323974, -6.619676026}

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