2x^2-3x-29=0

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Solution for 2x^2-3x-29=0 equation: 


Simplifying
2x2 + -3x + -29 = 0

Reorder the terms:
-29 + -3x + 2x2 = 0

Solving
-29 + -3x + 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'.
-14.5 + -1.5x + x2 = 0

Move the constant term to the right:

Add '14.5' to each side of the equation.
-14.5 + -1.5x + 14.5 + x2 = 0 + 14.5

Reorder the terms:
-14.5 + 14.5 + -1.5x + x2 = 0 + 14.5

Combine like terms: -14.5 + 14.5 = 0.0
0.0 + -1.5x + x2 = 0 + 14.5
-1.5x + x2 = 0 + 14.5

Combine like terms: 0 + 14.5 = 14.5
-1.5x + x2 = 14.5

The x term is -1.5x.  Take half its coefficient (-0.75).
Square it (0.5625) and add it to both sides.

Add '0.5625' to each side of the equation.
-1.5x + 0.5625 + x2 = 14.5 + 0.5625

Reorder the terms:
0.5625 + -1.5x + x2 = 14.5 + 0.5625

Combine like terms: 14.5 + 0.5625 = 15.0625
0.5625 + -1.5x + x2 = 15.0625

Factor a perfect square on the left side:
(x + -0.75)(x + -0.75) = 15.0625

Calculate the square root of the right side: 3.881043674

Break this problem into two subproblems by setting 
(x + -0.75) equal to 3.881043674 and -3.881043674.


Subproblem 1
x + -0.75 = 3.881043674

Simplifying
x + -0.75 = 3.881043674

Reorder the terms:
-0.75 + x = 3.881043674

Solving
-0.75 + x = 3.881043674

Solving for variable 'x'.

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

Add '0.75' to each side of the equation.
-0.75 + 0.75 + x = 3.881043674 + 0.75

Combine like terms: -0.75 + 0.75 = 0.00
0.00 + x = 3.881043674 + 0.75
x = 3.881043674 + 0.75

Combine like terms: 3.881043674 + 0.75 = 4.631043674
x = 4.631043674

Simplifying
x = 4.631043674


Subproblem 2
x + -0.75 = -3.881043674

Simplifying
x + -0.75 = -3.881043674

Reorder the terms:
-0.75 + x = -3.881043674

Solving
-0.75 + x = -3.881043674

Solving for variable 'x'.

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

Add '0.75' to each side of the equation.
-0.75 + 0.75 + x = -3.881043674 + 0.75

Combine like terms: -0.75 + 0.75 = 0.00
0.00 + x = -3.881043674 + 0.75
x = -3.881043674 + 0.75

Combine like terms: -3.881043674 + 0.75 = -3.131043674
x = -3.131043674

Simplifying
x = -3.131043674


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.631043674, -3.131043674}

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