0=.0119x^2-.308x-5.0003

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Solution for 0=.0119x^2-.308x-5.0003 equation:


Simplifying
0 = 0.0119x2 + -0.308x + -5.0003

Reorder the terms:
0 = -5.0003 + -0.308x + 0.0119x2

Solving
0 = -5.0003 + -0.308x + 0.0119x2

Solving for variable 'x'.

Combine like terms: 0 + 5.0003 = 5.0003
5.0003 + 0.308x + -0.0119x2 = -5.0003 + -0.308x + 0.0119x2 + 5.0003 + 0.308x + -0.0119x2

Reorder the terms:
5.0003 + 0.308x + -0.0119x2 = -5.0003 + 5.0003 + -0.308x + 0.308x + 0.0119x2 + -0.0119x2

Combine like terms: -5.0003 + 5.0003 = 0.0000
5.0003 + 0.308x + -0.0119x2 = 0.0000 + -0.308x + 0.308x + 0.0119x2 + -0.0119x2
5.0003 + 0.308x + -0.0119x2 = -0.308x + 0.308x + 0.0119x2 + -0.0119x2

Combine like terms: -0.308x + 0.308x = 0.000
5.0003 + 0.308x + -0.0119x2 = 0.000 + 0.0119x2 + -0.0119x2
5.0003 + 0.308x + -0.0119x2 = 0.0119x2 + -0.0119x2

Combine like terms: 0.0119x2 + -0.0119x2 = 0.0000
5.0003 + 0.308x + -0.0119x2 = 0.0000

Begin completing the square.  Divide all terms by
-0.0119 the coefficient of the squared term: 

Divide each side by '-0.0119'.
-420.1932773 + -25.88235294x + x2 = 0

Move the constant term to the right:

Add '420.1932773' to each side of the equation.
-420.1932773 + -25.88235294x + 420.1932773 + x2 = 0 + 420.1932773

Reorder the terms:
-420.1932773 + 420.1932773 + -25.88235294x + x2 = 0 + 420.1932773

Combine like terms: -420.1932773 + 420.1932773 = 0.0000000
0.0000000 + -25.88235294x + x2 = 0 + 420.1932773
-25.88235294x + x2 = 0 + 420.1932773

Combine like terms: 0 + 420.1932773 = 420.1932773
-25.88235294x + x2 = 420.1932773

The x term is -25.88235294x.  Take half its coefficient (-12.94117647).
Square it (167.4740484) and add it to both sides.

Add '167.4740484' to each side of the equation.
-25.88235294x + 167.4740484 + x2 = 420.1932773 + 167.4740484

Reorder the terms:
167.4740484 + -25.88235294x + x2 = 420.1932773 + 167.4740484

Combine like terms: 420.1932773 + 167.4740484 = 587.6673257
167.4740484 + -25.88235294x + x2 = 587.6673257

Factor a perfect square on the left side:
(x + -12.94117647)(x + -12.94117647) = 587.6673257

Calculate the square root of the right side: 24.241850707

Break this problem into two subproblems by setting 
(x + -12.94117647) equal to 24.241850707 and -24.241850707.

Subproblem 1

x + -12.94117647 = 24.241850707 Simplifying x + -12.94117647 = 24.241850707 Reorder the terms: -12.94117647 + x = 24.241850707 Solving -12.94117647 + x = 24.241850707 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12.94117647' to each side of the equation. -12.94117647 + 12.94117647 + x = 24.241850707 + 12.94117647 Combine like terms: -12.94117647 + 12.94117647 = 0.00000000 0.00000000 + x = 24.241850707 + 12.94117647 x = 24.241850707 + 12.94117647 Combine like terms: 24.241850707 + 12.94117647 = 37.183027177 x = 37.183027177 Simplifying x = 37.183027177

Subproblem 2

x + -12.94117647 = -24.241850707 Simplifying x + -12.94117647 = -24.241850707 Reorder the terms: -12.94117647 + x = -24.241850707 Solving -12.94117647 + x = -24.241850707 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12.94117647' to each side of the equation. -12.94117647 + 12.94117647 + x = -24.241850707 + 12.94117647 Combine like terms: -12.94117647 + 12.94117647 = 0.00000000 0.00000000 + x = -24.241850707 + 12.94117647 x = -24.241850707 + 12.94117647 Combine like terms: -24.241850707 + 12.94117647 = -11.300674237 x = -11.300674237 Simplifying x = -11.300674237

Solution

The solution to the problem is based on the solutions from the subproblems. x = {37.183027177, -11.300674237}

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