8x^2+73x+70=0

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Solution for 8x^2+73x+70=0 equation: 


Simplifying
8x2 + 73x + 70 = 0

Reorder the terms:
70 + 73x + 8x2 = 0

Solving
70 + 73x + 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'.
8.75 + 9.125x + x2 = 0

Move the constant term to the right:

Add '-8.75' to each side of the equation.
8.75 + 9.125x + -8.75 + x2 = 0 + -8.75

Reorder the terms:
8.75 + -8.75 + 9.125x + x2 = 0 + -8.75

Combine like terms: 8.75 + -8.75 = 0.00
0.00 + 9.125x + x2 = 0 + -8.75
9.125x + x2 = 0 + -8.75

Combine like terms: 0 + -8.75 = -8.75
9.125x + x2 = -8.75

The x term is 9.125x.  Take half its coefficient (4.5625).
Square it (20.81640625) and add it to both sides.

Add '20.81640625' to each side of the equation.
9.125x + 20.81640625 + x2 = -8.75 + 20.81640625

Reorder the terms:
20.81640625 + 9.125x + x2 = -8.75 + 20.81640625

Combine like terms: -8.75 + 20.81640625 = 12.06640625
20.81640625 + 9.125x + x2 = 12.06640625

Factor a perfect square on the left side:
(x + 4.5625)(x + 4.5625) = 12.06640625

Calculate the square root of the right side: 3.473673308

Break this problem into two subproblems by setting 
(x + 4.5625) equal to 3.473673308 and -3.473673308.


Subproblem 1
x + 4.5625 = 3.473673308

Simplifying
x + 4.5625 = 3.473673308

Reorder the terms:
4.5625 + x = 3.473673308

Solving
4.5625 + x = 3.473673308

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-4.5625' to each side of the equation.
4.5625 + -4.5625 + x = 3.473673308 + -4.5625

Combine like terms: 4.5625 + -4.5625 = 0.0000
0.0000 + x = 3.473673308 + -4.5625
x = 3.473673308 + -4.5625

Combine like terms: 3.473673308 + -4.5625 = -1.088826692
x = -1.088826692

Simplifying
x = -1.088826692


Subproblem 2
x + 4.5625 = -3.473673308

Simplifying
x + 4.5625 = -3.473673308

Reorder the terms:
4.5625 + x = -3.473673308

Solving
4.5625 + x = -3.473673308

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-4.5625' to each side of the equation.
4.5625 + -4.5625 + x = -3.473673308 + -4.5625

Combine like terms: 4.5625 + -4.5625 = 0.0000
0.0000 + x = -3.473673308 + -4.5625
x = -3.473673308 + -4.5625

Combine like terms: -3.473673308 + -4.5625 = -8.036173308
x = -8.036173308

Simplifying
x = -8.036173308


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-1.088826692, -8.036173308}

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