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 = 57.25
72.25 + -17x + x2 = 57.25

Factor a perfect square on the left side:
(x + -8.5)(x + -8.5) = 57.25

Calculate the square root of the right side: 7.566372975

Break this problem into two subproblems by setting 
(x + -8.5) equal to 7.566372975 and -7.566372975.


Subproblem 1
x + -8.5 = 7.566372975

Simplifying
x + -8.5 = 7.566372975

Reorder the terms:
-8.5 + x = 7.566372975

Solving
-8.5 + x = 7.566372975

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 = 7.566372975 + 8.5

Combine like terms: -8.5 + 8.5 = 0.0
0.0 + x = 7.566372975 + 8.5
x = 7.566372975 + 8.5

Combine like terms: 7.566372975 + 8.5 = 16.066372975
x = 16.066372975

Simplifying
x = 16.066372975


Subproblem 2
x + -8.5 = -7.566372975

Simplifying
x + -8.5 = -7.566372975

Reorder the terms:
-8.5 + x = -7.566372975

Solving
-8.5 + x = -7.566372975

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 = -7.566372975 + 8.5

Combine like terms: -8.5 + 8.5 = 0.0
0.0 + x = -7.566372975 + 8.5
x = -7.566372975 + 8.5

Combine like terms: -7.566372975 + 8.5 = 0.933627025
x = 0.933627025

Simplifying
x = 0.933627025


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {16.066372975, 0.933627025}
Solution
x = {16.066372975, 0.933627025}

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