2x^2+16x-31=0

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Solution for 2x^2+16x-31=0 equation:


Simplifying
2x2 + 16x + -31 = 0

Reorder the terms:
-31 + 16x + 2x2 = 0

Solving
-31 + 16x + 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'.
-15.5 + 8x + x2 = 0

Move the constant term to the right:

Add '15.5' to each side of the equation.
-15.5 + 8x + 15.5 + x2 = 0 + 15.5

Reorder the terms:
-15.5 + 15.5 + 8x + x2 = 0 + 15.5

Combine like terms: -15.5 + 15.5 = 0.0
0.0 + 8x + x2 = 0 + 15.5
8x + x2 = 0 + 15.5

Combine like terms: 0 + 15.5 = 15.5
8x + x2 = 15.5

The x term is 8x.  Take half its coefficient (4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
8x + 16 + x2 = 15.5 + 16

Reorder the terms:
16 + 8x + x2 = 15.5 + 16

Combine like terms: 15.5 + 16 = 31.5
16 + 8x + x2 = 31.5

Factor a perfect square on the left side:
(x + 4)(x + 4) = 31.5

Calculate the square root of the right side: 5.61248608

Break this problem into two subproblems by setting 
(x + 4) equal to 5.61248608 and -5.61248608.

Subproblem 1

x + 4 = 5.61248608 Simplifying x + 4 = 5.61248608 Reorder the terms: 4 + x = 5.61248608 Solving 4 + x = 5.61248608 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = 5.61248608 + -4 Combine like terms: 4 + -4 = 0 0 + x = 5.61248608 + -4 x = 5.61248608 + -4 Combine like terms: 5.61248608 + -4 = 1.61248608 x = 1.61248608 Simplifying x = 1.61248608

Subproblem 2

x + 4 = -5.61248608 Simplifying x + 4 = -5.61248608 Reorder the terms: 4 + x = -5.61248608 Solving 4 + x = -5.61248608 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = -5.61248608 + -4 Combine like terms: 4 + -4 = 0 0 + x = -5.61248608 + -4 x = -5.61248608 + -4 Combine like terms: -5.61248608 + -4 = -9.61248608 x = -9.61248608 Simplifying x = -9.61248608

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.61248608, -9.61248608}

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