2x^2-29x-30=0

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Solution for 2x^2-29x-30=0 equation:


Simplifying
2x2 + -29x + -30 = 0

Reorder the terms:
-30 + -29x + 2x2 = 0

Solving
-30 + -29x + 2x2 = 0

Solving for variable 'x'.

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

Divide each side by '2'.
-15 + -14.5x + x2 = 0

Move the constant term to the right:

Add '15' to each side of the equation.
-15 + -14.5x + 15 + x2 = 0 + 15

Reorder the terms:
-15 + 15 + -14.5x + x2 = 0 + 15

Combine like terms: -15 + 15 = 0
0 + -14.5x + x2 = 0 + 15
-14.5x + x2 = 0 + 15

Combine like terms: 0 + 15 = 15
-14.5x + x2 = 15

The x term is -14.5x.  Take half its coefficient (-7.25).
Square it (52.5625) and add it to both sides.

Add '52.5625' to each side of the equation.
-14.5x + 52.5625 + x2 = 15 + 52.5625

Reorder the terms:
52.5625 + -14.5x + x2 = 15 + 52.5625

Combine like terms: 15 + 52.5625 = 67.5625
52.5625 + -14.5x + x2 = 67.5625

Factor a perfect square on the left side:
(x + -7.25)(x + -7.25) = 67.5625

Calculate the square root of the right side: 8.219641111

Break this problem into two subproblems by setting 
(x + -7.25) equal to 8.219641111 and -8.219641111.


Subproblem 1
x + -7.25 = 8.219641111

Simplifying
x + -7.25 = 8.219641111

Reorder the terms:
-7.25 + x = 8.219641111

Solving
-7.25 + x = 8.219641111

Solving for variable 'x'.

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

Add '7.25' to each side of the equation.
-7.25 + 7.25 + x = 8.219641111 + 7.25

Combine like terms: -7.25 + 7.25 = 0.00
0.00 + x = 8.219641111 + 7.25
x = 8.219641111 + 7.25

Combine like terms: 8.219641111 + 7.25 = 15.469641111
x = 15.469641111

Simplifying
x = 15.469641111


Subproblem 2
x + -7.25 = -8.219641111

Simplifying
x + -7.25 = -8.219641111

Reorder the terms:
-7.25 + x = -8.219641111

Solving
-7.25 + x = -8.219641111

Solving for variable 'x'.

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

Add '7.25' to each side of the equation.
-7.25 + 7.25 + x = -8.219641111 + 7.25

Combine like terms: -7.25 + 7.25 = 0.00
0.00 + x = -8.219641111 + 7.25
x = -8.219641111 + 7.25

Combine like terms: -8.219641111 + 7.25 = -0.969641111
x = -0.969641111

Simplifying
x = -0.969641111


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {15.469641111, -0.969641111}

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