4x^2+70x+90=0

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Solution for 4x^2+70x+90=0 equation: 


Simplifying
4x2 + 70x + 90 = 0

Reorder the terms:
90 + 70x + 4x2 = 0

Solving
90 + 70x + 4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(45 + 35x + 2x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(45 + 35x + 2x2)' equal to zero and attempt to solve:

Simplifying
45 + 35x + 2x2 = 0

Solving
45 + 35x + 2x2 = 0

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

Divide each side by '2'.
22.5 + 17.5x + x2 = 0

Move the constant term to the right:

Add '-22.5' to each side of the equation.
22.5 + 17.5x + -22.5 + x2 = 0 + -22.5

Reorder the terms:
22.5 + -22.5 + 17.5x + x2 = 0 + -22.5

Combine like terms: 22.5 + -22.5 = 0.0
0.0 + 17.5x + x2 = 0 + -22.5
17.5x + x2 = 0 + -22.5

Combine like terms: 0 + -22.5 = -22.5
17.5x + x2 = -22.5

The x term is 17.5x.  Take half its coefficient (8.75).
Square it (76.5625) and add it to both sides.

Add '76.5625' to each side of the equation.
17.5x + 76.5625 + x2 = -22.5 + 76.5625

Reorder the terms:
76.5625 + 17.5x + x2 = -22.5 + 76.5625

Combine like terms: -22.5 + 76.5625 = 54.0625
76.5625 + 17.5x + x2 = 54.0625

Factor a perfect square on the left side:
(x + 8.75)(x + 8.75) = 54.0625

Calculate the square root of the right side: 7.352720585

Break this problem into two subproblems by setting 
(x + 8.75) equal to 7.352720585 and -7.352720585.


Subproblem 1
x + 8.75 = 7.352720585

Simplifying
x + 8.75 = 7.352720585

Reorder the terms:
8.75 + x = 7.352720585

Solving
8.75 + x = 7.352720585

Solving for variable 'x'.

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

Add '-8.75' to each side of the equation.
8.75 + -8.75 + x = 7.352720585 + -8.75

Combine like terms: 8.75 + -8.75 = 0.00
0.00 + x = 7.352720585 + -8.75
x = 7.352720585 + -8.75

Combine like terms: 7.352720585 + -8.75 = -1.397279415
x = -1.397279415

Simplifying
x = -1.397279415


Subproblem 2
x + 8.75 = -7.352720585

Simplifying
x + 8.75 = -7.352720585

Reorder the terms:
8.75 + x = -7.352720585

Solving
8.75 + x = -7.352720585

Solving for variable 'x'.

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

Add '-8.75' to each side of the equation.
8.75 + -8.75 + x = -7.352720585 + -8.75

Combine like terms: 8.75 + -8.75 = 0.00
0.00 + x = -7.352720585 + -8.75
x = -7.352720585 + -8.75

Combine like terms: -7.352720585 + -8.75 = -16.102720585
x = -16.102720585

Simplifying
x = -16.102720585


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-1.397279415, -16.102720585}
Solution
x = {-1.397279415, -16.102720585}

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