2x^2+34x-30=0

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Solution for 2x^2+34x-30=0 equation: 


Simplifying
2x2 + 34x + -30 = 0

Reorder the terms:
-30 + 34x + 2x2 = 0

Solving
-30 + 34x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-15 + 17x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-15 + 17x + x2)' equal to zero and attempt to solve:

Simplifying
-15 + 17x + x2 = 0

Solving
-15 + 17x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '15' to each side of the equation.
-15 + 17x + 15 + x2 = 0 + 15

Reorder the terms:
-15 + 15 + 17x + x2 = 0 + 15

Combine like terms: -15 + 15 = 0
0 + 17x + x2 = 0 + 15
17x + x2 = 0 + 15

Combine like terms: 0 + 15 = 15
17x + x2 = 15

The x term is 17x.  Take half its coefficient (8.5).
Square it (72.25) and add it to both sides.

Add '72.25' to each side of the equation.
17x + 72.25 + x2 = 15 + 72.25

Reorder the terms:
72.25 + 17x + x2 = 15 + 72.25

Combine like terms: 15 + 72.25 = 87.25
72.25 + 17x + x2 = 87.25

Factor a perfect square on the left side:
(x + 8.5)(x + 8.5) = 87.25

Calculate the square root of the right side: 9.340770846

Break this problem into two subproblems by setting 
(x + 8.5) equal to 9.340770846 and -9.340770846.


Subproblem 1
x + 8.5 = 9.340770846

Simplifying
x + 8.5 = 9.340770846

Reorder the terms:
8.5 + x = 9.340770846

Solving
8.5 + x = 9.340770846

Solving for variable 'x'.

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

Add '-8.5' to each side of the equation.
8.5 + -8.5 + x = 9.340770846 + -8.5

Combine like terms: 8.5 + -8.5 = 0.0
0.0 + x = 9.340770846 + -8.5
x = 9.340770846 + -8.5

Combine like terms: 9.340770846 + -8.5 = 0.840770846
x = 0.840770846

Simplifying
x = 0.840770846


Subproblem 2
x + 8.5 = -9.340770846

Simplifying
x + 8.5 = -9.340770846

Reorder the terms:
8.5 + x = -9.340770846

Solving
8.5 + x = -9.340770846

Solving for variable 'x'.

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

Add '-8.5' to each side of the equation.
8.5 + -8.5 + x = -9.340770846 + -8.5

Combine like terms: 8.5 + -8.5 = 0.0
0.0 + x = -9.340770846 + -8.5
x = -9.340770846 + -8.5

Combine like terms: -9.340770846 + -8.5 = -17.840770846
x = -17.840770846

Simplifying
x = -17.840770846


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.840770846, -17.840770846}
Solution
x = {0.840770846, -17.840770846}

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