15000x^2-167.76x-747.4=0

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Solution for 15000x^2-167.76x-747.4=0 equation: 


Simplifying
15000x2 + -167.76x + -747.4 = 0

Reorder the terms:
-747.4 + -167.76x + 15000x2 = 0

Solving
-747.4 + -167.76x + 15000x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
15000 the coefficient of the squared term: 

Divide each side by '15000'.
-0.04982666667 + -0.011184x + x2 = 0

Move the constant term to the right:

Add '0.04982666667' to each side of the equation.
-0.04982666667 + -0.011184x + 0.04982666667 + x2 = 0 + 0.04982666667

Reorder the terms:
-0.04982666667 + 0.04982666667 + -0.011184x + x2 = 0 + 0.04982666667

Combine like terms: -0.04982666667 + 0.04982666667 = 0.00000000000
0.00000000000 + -0.011184x + x2 = 0 + 0.04982666667
-0.011184x + x2 = 0 + 0.04982666667

Combine like terms: 0 + 0.04982666667 = 0.04982666667
-0.011184x + x2 = 0.04982666667

The x term is -0.011184x.  Take half its coefficient (-0.005592).
Square it (0.000031270464) and add it to both sides.

Add '0.000031270464' to each side of the equation.
-0.011184x + 0.000031270464 + x2 = 0.04982666667 + 0.000031270464

Reorder the terms:
0.000031270464 + -0.011184x + x2 = 0.04982666667 + 0.000031270464

Combine like terms: 0.04982666667 + 0.000031270464 = 0.049857937134
0.000031270464 + -0.011184x + x2 = 0.049857937134

Factor a perfect square on the left side:
(x + -0.005592)(x + -0.005592) = 0.049857937134

Calculate the square root of the right side: 0.22328891

Break this problem into two subproblems by setting 
(x + -0.005592) equal to 0.22328891 and -0.22328891.


Subproblem 1
x + -0.005592 = 0.22328891

Simplifying
x + -0.005592 = 0.22328891

Reorder the terms:
-0.005592 + x = 0.22328891

Solving
-0.005592 + x = 0.22328891

Solving for variable 'x'.

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

Add '0.005592' to each side of the equation.
-0.005592 + 0.005592 + x = 0.22328891 + 0.005592

Combine like terms: -0.005592 + 0.005592 = 0.000000
0.000000 + x = 0.22328891 + 0.005592
x = 0.22328891 + 0.005592

Combine like terms: 0.22328891 + 0.005592 = 0.22888091
x = 0.22888091

Simplifying
x = 0.22888091


Subproblem 2
x + -0.005592 = -0.22328891

Simplifying
x + -0.005592 = -0.22328891

Reorder the terms:
-0.005592 + x = -0.22328891

Solving
-0.005592 + x = -0.22328891

Solving for variable 'x'.

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

Add '0.005592' to each side of the equation.
-0.005592 + 0.005592 + x = -0.22328891 + 0.005592

Combine like terms: -0.005592 + 0.005592 = 0.000000
0.000000 + x = -0.22328891 + 0.005592
x = -0.22328891 + 0.005592

Combine like terms: -0.22328891 + 0.005592 = -0.21769691
x = -0.21769691

Simplifying
x = -0.21769691


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.22888091, -0.21769691}

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