10x^2+90x+14=0

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Solution for 10x^2+90x+14=0 equation: 


Simplifying
10x2 + 90x + 14 = 0

Reorder the terms:
14 + 90x + 10x2 = 0

Solving
14 + 90x + 10x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(7 + 45x + 5x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(7 + 45x + 5x2)' equal to zero and attempt to solve:

Simplifying
7 + 45x + 5x2 = 0

Solving
7 + 45x + 5x2 = 0

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

Divide each side by '5'.
1.4 + 9x + x2 = 0

Move the constant term to the right:

Add '-1.4' to each side of the equation.
1.4 + 9x + -1.4 + x2 = 0 + -1.4

Reorder the terms:
1.4 + -1.4 + 9x + x2 = 0 + -1.4

Combine like terms: 1.4 + -1.4 = 0.0
0.0 + 9x + x2 = 0 + -1.4
9x + x2 = 0 + -1.4

Combine like terms: 0 + -1.4 = -1.4
9x + x2 = -1.4

The x term is 9x.  Take half its coefficient (4.5).
Square it (20.25) and add it to both sides.

Add '20.25' to each side of the equation.
9x + 20.25 + x2 = -1.4 + 20.25

Reorder the terms:
20.25 + 9x + x2 = -1.4 + 20.25

Combine like terms: -1.4 + 20.25 = 18.85
20.25 + 9x + x2 = 18.85

Factor a perfect square on the left side:
(x + 4.5)(x + 4.5) = 18.85

Calculate the square root of the right side: 4.341658669

Break this problem into two subproblems by setting 
(x + 4.5) equal to 4.341658669 and -4.341658669.


Subproblem 1
x + 4.5 = 4.341658669

Simplifying
x + 4.5 = 4.341658669

Reorder the terms:
4.5 + x = 4.341658669

Solving
4.5 + x = 4.341658669

Solving for variable 'x'.

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

Add '-4.5' to each side of the equation.
4.5 + -4.5 + x = 4.341658669 + -4.5

Combine like terms: 4.5 + -4.5 = 0.0
0.0 + x = 4.341658669 + -4.5
x = 4.341658669 + -4.5

Combine like terms: 4.341658669 + -4.5 = -0.158341331
x = -0.158341331

Simplifying
x = -0.158341331


Subproblem 2
x + 4.5 = -4.341658669

Simplifying
x + 4.5 = -4.341658669

Reorder the terms:
4.5 + x = -4.341658669

Solving
4.5 + x = -4.341658669

Solving for variable 'x'.

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

Add '-4.5' to each side of the equation.
4.5 + -4.5 + x = -4.341658669 + -4.5

Combine like terms: 4.5 + -4.5 = 0.0
0.0 + x = -4.341658669 + -4.5
x = -4.341658669 + -4.5

Combine like terms: -4.341658669 + -4.5 = -8.841658669
x = -8.841658669

Simplifying
x = -8.841658669


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.158341331, -8.841658669}
Solution
x = {-0.158341331, -8.841658669}

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