2x^2+31x-21=0

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Solution for 2x^2+31x-21=0 equation:


Simplifying
2x2 + 31x + -21 = 0

Reorder the terms:
-21 + 31x + 2x2 = 0

Solving
-21 + 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'.
-10.5 + 15.5x + x2 = 0

Move the constant term to the right:

Add '10.5' to each side of the equation.
-10.5 + 15.5x + 10.5 + x2 = 0 + 10.5

Reorder the terms:
-10.5 + 10.5 + 15.5x + x2 = 0 + 10.5

Combine like terms: -10.5 + 10.5 = 0.0
0.0 + 15.5x + x2 = 0 + 10.5
15.5x + x2 = 0 + 10.5

Combine like terms: 0 + 10.5 = 10.5
15.5x + x2 = 10.5

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 = 10.5 + 60.0625

Reorder the terms:
60.0625 + 15.5x + x2 = 10.5 + 60.0625

Combine like terms: 10.5 + 60.0625 = 70.5625
60.0625 + 15.5x + x2 = 70.5625

Factor a perfect square on the left side:
(x + 7.75)(x + 7.75) = 70.5625

Calculate the square root of the right side: 8.400148808

Break this problem into two subproblems by setting 
(x + 7.75) equal to 8.400148808 and -8.400148808.

Subproblem 1

x + 7.75 = 8.400148808 Simplifying x + 7.75 = 8.400148808 Reorder the terms: 7.75 + x = 8.400148808 Solving 7.75 + x = 8.400148808 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 = 8.400148808 + -7.75 Combine like terms: 7.75 + -7.75 = 0.00 0.00 + x = 8.400148808 + -7.75 x = 8.400148808 + -7.75 Combine like terms: 8.400148808 + -7.75 = 0.650148808 x = 0.650148808 Simplifying x = 0.650148808

Subproblem 2

x + 7.75 = -8.400148808 Simplifying x + 7.75 = -8.400148808 Reorder the terms: 7.75 + x = -8.400148808 Solving 7.75 + x = -8.400148808 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 = -8.400148808 + -7.75 Combine like terms: 7.75 + -7.75 = 0.00 0.00 + x = -8.400148808 + -7.75 x = -8.400148808 + -7.75 Combine like terms: -8.400148808 + -7.75 = -16.150148808 x = -16.150148808 Simplifying x = -16.150148808

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.650148808, -16.150148808}

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