2x^2+29x-9=0

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Solution for 2x^2+29x-9=0 equation:


Simplifying
2x2 + 29x + -9 = 0

Reorder the terms:
-9 + 29x + 2x2 = 0

Solving
-9 + 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'.
-4.5 + 14.5x + x2 = 0

Move the constant term to the right:

Add '4.5' to each side of the equation.
-4.5 + 14.5x + 4.5 + x2 = 0 + 4.5

Reorder the terms:
-4.5 + 4.5 + 14.5x + x2 = 0 + 4.5

Combine like terms: -4.5 + 4.5 = 0.0
0.0 + 14.5x + x2 = 0 + 4.5
14.5x + x2 = 0 + 4.5

Combine like terms: 0 + 4.5 = 4.5
14.5x + x2 = 4.5

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 = 4.5 + 52.5625

Reorder the terms:
52.5625 + 14.5x + x2 = 4.5 + 52.5625

Combine like terms: 4.5 + 52.5625 = 57.0625
52.5625 + 14.5x + x2 = 57.0625

Factor a perfect square on the left side:
(x + 7.25)(x + 7.25) = 57.0625

Calculate the square root of the right side: 7.553972465

Break this problem into two subproblems by setting 
(x + 7.25) equal to 7.553972465 and -7.553972465.

Subproblem 1

x + 7.25 = 7.553972465 Simplifying x + 7.25 = 7.553972465 Reorder the terms: 7.25 + x = 7.553972465 Solving 7.25 + x = 7.553972465 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 = 7.553972465 + -7.25 Combine like terms: 7.25 + -7.25 = 0.00 0.00 + x = 7.553972465 + -7.25 x = 7.553972465 + -7.25 Combine like terms: 7.553972465 + -7.25 = 0.303972465 x = 0.303972465 Simplifying x = 0.303972465

Subproblem 2

x + 7.25 = -7.553972465 Simplifying x + 7.25 = -7.553972465 Reorder the terms: 7.25 + x = -7.553972465 Solving 7.25 + x = -7.553972465 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 = -7.553972465 + -7.25 Combine like terms: 7.25 + -7.25 = 0.00 0.00 + x = -7.553972465 + -7.25 x = -7.553972465 + -7.25 Combine like terms: -7.553972465 + -7.25 = -14.803972465 x = -14.803972465 Simplifying x = -14.803972465

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.303972465, -14.803972465}

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