2x^2+31x-6.9=0

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Solution for 2x^2+31x-6.9=0 equation:


Simplifying
2x2 + 31x + -6.9 = 0

Reorder the terms:
-6.9 + 31x + 2x2 = 0

Solving
-6.9 + 31x + 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'.
-3.45 + 15.5x + x2 = 0

Move the constant term to the right:

Add '3.45' to each side of the equation.
-3.45 + 15.5x + 3.45 + x2 = 0 + 3.45

Reorder the terms:
-3.45 + 3.45 + 15.5x + x2 = 0 + 3.45

Combine like terms: -3.45 + 3.45 = 0.00
0.00 + 15.5x + x2 = 0 + 3.45
15.5x + x2 = 0 + 3.45

Combine like terms: 0 + 3.45 = 3.45
15.5x + x2 = 3.45

The x term is 15.5x.  Take half its coefficient (7.75).
Square it (60.0625) and add it to both sides.

Add '60.0625' to each side of the equation.
15.5x + 60.0625 + x2 = 3.45 + 60.0625

Reorder the terms:
60.0625 + 15.5x + x2 = 3.45 + 60.0625

Combine like terms: 3.45 + 60.0625 = 63.5125
60.0625 + 15.5x + x2 = 63.5125

Factor a perfect square on the left side:
(x + 7.75)(x + 7.75) = 63.5125

Calculate the square root of the right side: 7.969473006

Break this problem into two subproblems by setting 
(x + 7.75) equal to 7.969473006 and -7.969473006.

Subproblem 1

x + 7.75 = 7.969473006 Simplifying x + 7.75 = 7.969473006 Reorder the terms: 7.75 + x = 7.969473006 Solving 7.75 + x = 7.969473006 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7.75' to each side of the equation. 7.75 + -7.75 + x = 7.969473006 + -7.75 Combine like terms: 7.75 + -7.75 = 0.00 0.00 + x = 7.969473006 + -7.75 x = 7.969473006 + -7.75 Combine like terms: 7.969473006 + -7.75 = 0.219473006 x = 0.219473006 Simplifying x = 0.219473006

Subproblem 2

x + 7.75 = -7.969473006 Simplifying x + 7.75 = -7.969473006 Reorder the terms: 7.75 + x = -7.969473006 Solving 7.75 + x = -7.969473006 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7.75' to each side of the equation. 7.75 + -7.75 + x = -7.969473006 + -7.75 Combine like terms: 7.75 + -7.75 = 0.00 0.00 + x = -7.969473006 + -7.75 x = -7.969473006 + -7.75 Combine like terms: -7.969473006 + -7.75 = -15.719473006 x = -15.719473006 Simplifying x = -15.719473006

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.219473006, -15.719473006}

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