2x^2-2=-5x-1

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Solution for 2x^2-2=-5x-1 equation:


Simplifying
2x2 + -2 = -5x + -1

Reorder the terms:
-2 + 2x2 = -5x + -1

Reorder the terms:
-2 + 2x2 = -1 + -5x

Solving
-2 + 2x2 = -1 + -5x

Solving for variable 'x'.

Reorder the terms:
-2 + 1 + 5x + 2x2 = -1 + -5x + 1 + 5x

Combine like terms: -2 + 1 = -1
-1 + 5x + 2x2 = -1 + -5x + 1 + 5x

Reorder the terms:
-1 + 5x + 2x2 = -1 + 1 + -5x + 5x

Combine like terms: -1 + 1 = 0
-1 + 5x + 2x2 = 0 + -5x + 5x
-1 + 5x + 2x2 = -5x + 5x

Combine like terms: -5x + 5x = 0
-1 + 5x + 2x2 = 0

Begin completing the square.  Divide all terms by
2 the coefficient of the squared term: 

Divide each side by '2'.
-0.5 + 2.5x + x2 = 0

Move the constant term to the right:

Add '0.5' to each side of the equation.
-0.5 + 2.5x + 0.5 + x2 = 0 + 0.5

Reorder the terms:
-0.5 + 0.5 + 2.5x + x2 = 0 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + 2.5x + x2 = 0 + 0.5
2.5x + x2 = 0 + 0.5

Combine like terms: 0 + 0.5 = 0.5
2.5x + x2 = 0.5

The x term is 2.5x.  Take half its coefficient (1.25).
Square it (1.5625) and add it to both sides.

Add '1.5625' to each side of the equation.
2.5x + 1.5625 + x2 = 0.5 + 1.5625

Reorder the terms:
1.5625 + 2.5x + x2 = 0.5 + 1.5625

Combine like terms: 0.5 + 1.5625 = 2.0625
1.5625 + 2.5x + x2 = 2.0625

Factor a perfect square on the left side:
(x + 1.25)(x + 1.25) = 2.0625

Calculate the square root of the right side: 1.436140662

Break this problem into two subproblems by setting 
(x + 1.25) equal to 1.436140662 and -1.436140662.

Subproblem 1

x + 1.25 = 1.436140662 Simplifying x + 1.25 = 1.436140662 Reorder the terms: 1.25 + x = 1.436140662 Solving 1.25 + x = 1.436140662 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + x = 1.436140662 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = 1.436140662 + -1.25 x = 1.436140662 + -1.25 Combine like terms: 1.436140662 + -1.25 = 0.186140662 x = 0.186140662 Simplifying x = 0.186140662

Subproblem 2

x + 1.25 = -1.436140662 Simplifying x + 1.25 = -1.436140662 Reorder the terms: 1.25 + x = -1.436140662 Solving 1.25 + x = -1.436140662 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + x = -1.436140662 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = -1.436140662 + -1.25 x = -1.436140662 + -1.25 Combine like terms: -1.436140662 + -1.25 = -2.686140662 x = -2.686140662 Simplifying x = -2.686140662

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.186140662, -2.686140662}

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