2x^2+31x-6.7=0

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Solution for 2x^2+31x-6.7=0 equation:


Simplifying
2x2 + 31x + -6.7 = 0

Reorder the terms:
-6.7 + 31x + 2x2 = 0

Solving
-6.7 + 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'.
-3.35 + 15.5x + x2 = 0

Move the constant term to the right:

Add '3.35' to each side of the equation.
-3.35 + 15.5x + 3.35 + x2 = 0 + 3.35

Reorder the terms:
-3.35 + 3.35 + 15.5x + x2 = 0 + 3.35

Combine like terms: -3.35 + 3.35 = 0.00
0.00 + 15.5x + x2 = 0 + 3.35
15.5x + x2 = 0 + 3.35

Combine like terms: 0 + 3.35 = 3.35
15.5x + x2 = 3.35

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 = 3.35 + 60.0625

Reorder the terms:
60.0625 + 15.5x + x2 = 3.35 + 60.0625

Combine like terms: 3.35 + 60.0625 = 63.4125
60.0625 + 15.5x + x2 = 63.4125

Factor a perfect square on the left side:
(x + 7.75)(x + 7.75) = 63.4125

Calculate the square root of the right side: 7.963196594

Break this problem into two subproblems by setting 
(x + 7.75) equal to 7.963196594 and -7.963196594.

Subproblem 1

x + 7.75 = 7.963196594 Simplifying x + 7.75 = 7.963196594 Reorder the terms: 7.75 + x = 7.963196594 Solving 7.75 + x = 7.963196594 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 = 7.963196594 + -7.75 Combine like terms: 7.75 + -7.75 = 0.00 0.00 + x = 7.963196594 + -7.75 x = 7.963196594 + -7.75 Combine like terms: 7.963196594 + -7.75 = 0.213196594 x = 0.213196594 Simplifying x = 0.213196594

Subproblem 2

x + 7.75 = -7.963196594 Simplifying x + 7.75 = -7.963196594 Reorder the terms: 7.75 + x = -7.963196594 Solving 7.75 + x = -7.963196594 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 = -7.963196594 + -7.75 Combine like terms: 7.75 + -7.75 = 0.00 0.00 + x = -7.963196594 + -7.75 x = -7.963196594 + -7.75 Combine like terms: -7.963196594 + -7.75 = -15.713196594 x = -15.713196594 Simplifying x = -15.713196594

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.213196594, -15.713196594}

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