20x^2+14x-10=0

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Solution for 20x^2+14x-10=0 equation:


Simplifying
20x2 + 14x + -10 = 0

Reorder the terms:
-10 + 14x + 20x2 = 0

Solving
-10 + 14x + 20x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-5 + 7x + 10x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-5 + 7x + 10x2)' equal to zero and attempt to solve:

Simplifying
-5 + 7x + 10x2 = 0

Solving
-5 + 7x + 10x2 = 0

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

Divide each side by '10'.
-0.5 + 0.7x + x2 = 0.0

Move the constant term to the right:

Add '0.5' to each side of the equation.
-0.5 + 0.7x + 0.5 + x2 = 0.0 + 0.5

Reorder the terms:
-0.5 + 0.5 + 0.7x + x2 = 0.0 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + 0.7x + x2 = 0.0 + 0.5
0.7x + x2 = 0.0 + 0.5

Combine like terms: 0.0 + 0.5 = 0.5
0.7x + x2 = 0.5

The x term is 0.7x.  Take half its coefficient (0.35).
Square it (0.1225) and add it to both sides.

Add '0.1225' to each side of the equation.
0.7x + 0.1225 + x2 = 0.5 + 0.1225

Reorder the terms:
0.1225 + 0.7x + x2 = 0.5 + 0.1225

Combine like terms: 0.5 + 0.1225 = 0.6225
0.1225 + 0.7x + x2 = 0.6225

Factor a perfect square on the left side:
(x + 0.35)(x + 0.35) = 0.6225

Calculate the square root of the right side: 0.788986692

Break this problem into two subproblems by setting 
(x + 0.35) equal to 0.788986692 and -0.788986692.


Subproblem 1
x + 0.35 = 0.788986692

Simplifying
x + 0.35 = 0.788986692

Reorder the terms:
0.35 + x = 0.788986692

Solving
0.35 + x = 0.788986692

Solving for variable 'x'.

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

Add '-0.35' to each side of the equation.
0.35 + -0.35 + x = 0.788986692 + -0.35

Combine like terms: 0.35 + -0.35 = 0.00
0.00 + x = 0.788986692 + -0.35
x = 0.788986692 + -0.35

Combine like terms: 0.788986692 + -0.35 = 0.438986692
x = 0.438986692

Simplifying
x = 0.438986692


Subproblem 2
x + 0.35 = -0.788986692

Simplifying
x + 0.35 = -0.788986692

Reorder the terms:
0.35 + x = -0.788986692

Solving
0.35 + x = -0.788986692

Solving for variable 'x'.

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

Add '-0.35' to each side of the equation.
0.35 + -0.35 + x = -0.788986692 + -0.35

Combine like terms: 0.35 + -0.35 = 0.00
0.00 + x = -0.788986692 + -0.35
x = -0.788986692 + -0.35

Combine like terms: -0.788986692 + -0.35 = -1.138986692
x = -1.138986692

Simplifying
x = -1.138986692


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.438986692, -1.138986692}
Solution
x = {0.438986692, -1.138986692}

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