69.87x^2+12.94x-8.995=0

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Solution for 69.87x^2+12.94x-8.995=0 equation:


Simplifying
69.87x2 + 12.94x + -8.995 = 0

Reorder the terms:
-8.995 + 12.94x + 69.87x2 = 0

Solving
-8.995 + 12.94x + 69.87x2 = 0

Solving for variable 'x'.

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

Divide each side by '69.87'.
-0.1287390869 + 0.1852010877x + x2 = 0

Move the constant term to the right:

Add '0.1287390869' to each side of the equation.
-0.1287390869 + 0.1852010877x + 0.1287390869 + x2 = 0 + 0.1287390869

Reorder the terms:
-0.1287390869 + 0.1287390869 + 0.1852010877x + x2 = 0 + 0.1287390869

Combine like terms: -0.1287390869 + 0.1287390869 = 0.0000000000
0.0000000000 + 0.1852010877x + x2 = 0 + 0.1287390869
0.1852010877x + x2 = 0 + 0.1287390869

Combine like terms: 0 + 0.1287390869 = 0.1287390869
0.1852010877x + x2 = 0.1287390869

The x term is 0.1852010877x.  Take half its coefficient (0.09260054385).
Square it (0.008574860721) and add it to both sides.

Add '0.008574860721' to each side of the equation.
0.1852010877x + 0.008574860721 + x2 = 0.1287390869 + 0.008574860721

Reorder the terms:
0.008574860721 + 0.1852010877x + x2 = 0.1287390869 + 0.008574860721

Combine like terms: 0.1287390869 + 0.008574860721 = 0.137313947621
0.008574860721 + 0.1852010877x + x2 = 0.137313947621

Factor a perfect square on the left side:
(x + 0.09260054385)(x + 0.09260054385) = 0.137313947621

Calculate the square root of the right side: 0.370558966

Break this problem into two subproblems by setting 
(x + 0.09260054385) equal to 0.370558966 and -0.370558966.

Subproblem 1

x + 0.09260054385 = 0.370558966 Simplifying x + 0.09260054385 = 0.370558966 Reorder the terms: 0.09260054385 + x = 0.370558966 Solving 0.09260054385 + x = 0.370558966 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.09260054385' to each side of the equation. 0.09260054385 + -0.09260054385 + x = 0.370558966 + -0.09260054385 Combine like terms: 0.09260054385 + -0.09260054385 = 0.00000000000 0.00000000000 + x = 0.370558966 + -0.09260054385 x = 0.370558966 + -0.09260054385 Combine like terms: 0.370558966 + -0.09260054385 = 0.27795842215 x = 0.27795842215 Simplifying x = 0.27795842215

Subproblem 2

x + 0.09260054385 = -0.370558966 Simplifying x + 0.09260054385 = -0.370558966 Reorder the terms: 0.09260054385 + x = -0.370558966 Solving 0.09260054385 + x = -0.370558966 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.09260054385' to each side of the equation. 0.09260054385 + -0.09260054385 + x = -0.370558966 + -0.09260054385 Combine like terms: 0.09260054385 + -0.09260054385 = 0.00000000000 0.00000000000 + x = -0.370558966 + -0.09260054385 x = -0.370558966 + -0.09260054385 Combine like terms: -0.370558966 + -0.09260054385 = -0.46315950985 x = -0.46315950985 Simplifying x = -0.46315950985

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.27795842215, -0.46315950985}

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