x^2-3x-31=2

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


Simplifying
x2 + -3x + -31 = 2

Reorder the terms:
-31 + -3x + x2 = 2

Solving
-31 + -3x + x2 = 2

Solving for variable 'x'.

Reorder the terms:
-31 + -2 + -3x + x2 = 2 + -2

Combine like terms: -31 + -2 = -33
-33 + -3x + x2 = 2 + -2

Combine like terms: 2 + -2 = 0
-33 + -3x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '33' to each side of the equation.
-33 + -3x + 33 + x2 = 0 + 33

Reorder the terms:
-33 + 33 + -3x + x2 = 0 + 33

Combine like terms: -33 + 33 = 0
0 + -3x + x2 = 0 + 33
-3x + x2 = 0 + 33

Combine like terms: 0 + 33 = 33
-3x + x2 = 33

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 = 33 + 2.25

Reorder the terms:
2.25 + -3x + x2 = 33 + 2.25

Combine like terms: 33 + 2.25 = 35.25
2.25 + -3x + x2 = 35.25

Factor a perfect square on the left side:
(x + -1.5)(x + -1.5) = 35.25

Calculate the square root of the right side: 5.937171044

Break this problem into two subproblems by setting 
(x + -1.5) equal to 5.937171044 and -5.937171044.

Subproblem 1

x + -1.5 = 5.937171044 Simplifying x + -1.5 = 5.937171044 Reorder the terms: -1.5 + x = 5.937171044 Solving -1.5 + x = 5.937171044 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 = 5.937171044 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 5.937171044 + 1.5 x = 5.937171044 + 1.5 Combine like terms: 5.937171044 + 1.5 = 7.437171044 x = 7.437171044 Simplifying x = 7.437171044

Subproblem 2

x + -1.5 = -5.937171044 Simplifying x + -1.5 = -5.937171044 Reorder the terms: -1.5 + x = -5.937171044 Solving -1.5 + x = -5.937171044 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 = -5.937171044 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -5.937171044 + 1.5 x = -5.937171044 + 1.5 Combine like terms: -5.937171044 + 1.5 = -4.437171044 x = -4.437171044 Simplifying x = -4.437171044

Solution

The solution to the problem is based on the solutions from the subproblems. x = {7.437171044, -4.437171044}

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