x^2+29.4x-750=0

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Solution for x^2+29.4x-750=0 equation: 


Simplifying
x2 + 29.4x + -750 = 0

Reorder the terms:
-750 + 29.4x + x2 = 0

Solving
-750 + 29.4x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '750' to each side of the equation.
-750 + 29.4x + 750 + x2 = 0 + 750

Reorder the terms:
-750 + 750 + 29.4x + x2 = 0 + 750

Combine like terms: -750 + 750 = 0
0 + 29.4x + x2 = 0 + 750
29.4x + x2 = 0 + 750

Combine like terms: 0 + 750 = 750
29.4x + x2 = 750

The x term is 29.4x.  Take half its coefficient (14.7).
Square it (216.09) and add it to both sides.

Add '216.09' to each side of the equation.
29.4x + 216.09 + x2 = 750 + 216.09

Reorder the terms:
216.09 + 29.4x + x2 = 750 + 216.09

Combine like terms: 750 + 216.09 = 966.09
216.09 + 29.4x + x2 = 966.09

Factor a perfect square on the left side:
(x + 14.7)(x + 14.7) = 966.09

Calculate the square root of the right side: 31.081988353

Break this problem into two subproblems by setting 
(x + 14.7) equal to 31.081988353 and -31.081988353.


Subproblem 1
x + 14.7 = 31.081988353

Simplifying
x + 14.7 = 31.081988353

Reorder the terms:
14.7 + x = 31.081988353

Solving
14.7 + x = 31.081988353

Solving for variable 'x'.

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

Add '-14.7' to each side of the equation.
14.7 + -14.7 + x = 31.081988353 + -14.7

Combine like terms: 14.7 + -14.7 = 0.0
0.0 + x = 31.081988353 + -14.7
x = 31.081988353 + -14.7

Combine like terms: 31.081988353 + -14.7 = 16.381988353
x = 16.381988353

Simplifying
x = 16.381988353


Subproblem 2
x + 14.7 = -31.081988353

Simplifying
x + 14.7 = -31.081988353

Reorder the terms:
14.7 + x = -31.081988353

Solving
14.7 + x = -31.081988353

Solving for variable 'x'.

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

Add '-14.7' to each side of the equation.
14.7 + -14.7 + x = -31.081988353 + -14.7

Combine like terms: 14.7 + -14.7 = 0.0
0.0 + x = -31.081988353 + -14.7
x = -31.081988353 + -14.7

Combine like terms: -31.081988353 + -14.7 = -45.781988353
x = -45.781988353

Simplifying
x = -45.781988353


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {16.381988353, -45.781988353}

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