x^2-3x-31=0

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Solution for x^2-3x-31=0 equation:


Simplifying
x2 + -3x + -31 = 0

Reorder the terms:
-31 + -3x + x2 = 0

Solving
-31 + -3x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '31' to each side of the equation.
-31 + -3x + 31 + x2 = 0 + 31

Reorder the terms:
-31 + 31 + -3x + x2 = 0 + 31

Combine like terms: -31 + 31 = 0
0 + -3x + x2 = 0 + 31
-3x + x2 = 0 + 31

Combine like terms: 0 + 31 = 31
-3x + x2 = 31

The x term is -3x.  Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
-3x + 2.25 + x2 = 31 + 2.25

Reorder the terms:
2.25 + -3x + x2 = 31 + 2.25

Combine like terms: 31 + 2.25 = 33.25
2.25 + -3x + x2 = 33.25

Factor a perfect square on the left side:
(x + -1.5)(x + -1.5) = 33.25

Calculate the square root of the right side: 5.766281297

Break this problem into two subproblems by setting 
(x + -1.5) equal to 5.766281297 and -5.766281297.

Subproblem 1

x + -1.5 = 5.766281297 Simplifying x + -1.5 = 5.766281297 Reorder the terms: -1.5 + x = 5.766281297 Solving -1.5 + x = 5.766281297 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = 5.766281297 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 5.766281297 + 1.5 x = 5.766281297 + 1.5 Combine like terms: 5.766281297 + 1.5 = 7.266281297 x = 7.266281297 Simplifying x = 7.266281297

Subproblem 2

x + -1.5 = -5.766281297 Simplifying x + -1.5 = -5.766281297 Reorder the terms: -1.5 + x = -5.766281297 Solving -1.5 + x = -5.766281297 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = -5.766281297 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -5.766281297 + 1.5 x = -5.766281297 + 1.5 Combine like terms: -5.766281297 + 1.5 = -4.266281297 x = -4.266281297 Simplifying x = -4.266281297

Solution

The solution to the problem is based on the solutions from the subproblems. x = {7.266281297, -4.266281297}

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