60x^2+120x-70=0

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Solution for 60x^2+120x-70=0 equation: 


Simplifying
60x2 + 120x + -70 = 0

Reorder the terms:
-70 + 120x + 60x2 = 0

Solving
-70 + 120x + 60x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '10'.
10(-7 + 12x + 6x2) = 0

Ignore the factor 10.

Subproblem 1
Set the factor '(-7 + 12x + 6x2)' equal to zero and attempt to solve:

Simplifying
-7 + 12x + 6x2 = 0

Solving
-7 + 12x + 6x2 = 0

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

Divide each side by '6'.
-1.166666667 + 2x + x2 = 0

Move the constant term to the right:

Add '1.166666667' to each side of the equation.
-1.166666667 + 2x + 1.166666667 + x2 = 0 + 1.166666667

Reorder the terms:
-1.166666667 + 1.166666667 + 2x + x2 = 0 + 1.166666667

Combine like terms: -1.166666667 + 1.166666667 = 0.000000000
0.000000000 + 2x + x2 = 0 + 1.166666667
2x + x2 = 0 + 1.166666667

Combine like terms: 0 + 1.166666667 = 1.166666667
2x + x2 = 1.166666667

The x term is 2x.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2x + 1 + x2 = 1.166666667 + 1

Reorder the terms:
1 + 2x + x2 = 1.166666667 + 1

Combine like terms: 1.166666667 + 1 = 2.166666667
1 + 2x + x2 = 2.166666667

Factor a perfect square on the left side:
(x + 1)(x + 1) = 2.166666667

Calculate the square root of the right side: 1.471960145

Break this problem into two subproblems by setting 
(x + 1) equal to 1.471960145 and -1.471960145.


Subproblem 1
x + 1 = 1.471960145

Simplifying
x + 1 = 1.471960145

Reorder the terms:
1 + x = 1.471960145

Solving
1 + x = 1.471960145

Solving for variable 'x'.

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

Add '-1' to each side of the equation.
1 + -1 + x = 1.471960145 + -1

Combine like terms: 1 + -1 = 0
0 + x = 1.471960145 + -1
x = 1.471960145 + -1

Combine like terms: 1.471960145 + -1 = 0.471960145
x = 0.471960145

Simplifying
x = 0.471960145


Subproblem 2
x + 1 = -1.471960145

Simplifying
x + 1 = -1.471960145

Reorder the terms:
1 + x = -1.471960145

Solving
1 + x = -1.471960145

Solving for variable 'x'.

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

Add '-1' to each side of the equation.
1 + -1 + x = -1.471960145 + -1

Combine like terms: 1 + -1 = 0
0 + x = -1.471960145 + -1
x = -1.471960145 + -1

Combine like terms: -1.471960145 + -1 = -2.471960145
x = -2.471960145

Simplifying
x = -2.471960145


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.471960145, -2.471960145}
Solution
x = {0.471960145, -2.471960145}

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