-5x^2+x=-2

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


Simplifying
-5x2 + x = -2

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

Solving
x + -5x2 = -2

Solving for variable 'x'.

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

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

Begin completing the square.  Divide all terms by
-5 the coefficient of the squared term: 

Divide each side by '-5'.
-0.4 + -0.2x + x2 = 0

Move the constant term to the right:

Add '0.4' to each side of the equation.
-0.4 + -0.2x + 0.4 + x2 = 0 + 0.4

Reorder the terms:
-0.4 + 0.4 + -0.2x + x2 = 0 + 0.4

Combine like terms: -0.4 + 0.4 = 0.0
0.0 + -0.2x + x2 = 0 + 0.4
-0.2x + x2 = 0 + 0.4

Combine like terms: 0 + 0.4 = 0.4
-0.2x + x2 = 0.4

The x term is x.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-0.2x + 0.25 + x2 = 0.4 + 0.25

Reorder the terms:
0.25 + -0.2x + x2 = 0.4 + 0.25

Combine like terms: 0.4 + 0.25 = 0.65
0.25 + -0.2x + x2 = 0.65

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 0.65

Calculate the square root of the right side: 0.806225775

Break this problem into two subproblems by setting 
(x + 0.5) equal to 0.806225775 and -0.806225775.

Subproblem 1

x + 0.5 = 0.806225775 Simplifying x + 0.5 = 0.806225775 Reorder the terms: 0.5 + x = 0.806225775 Solving 0.5 + x = 0.806225775 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 0.806225775 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 0.806225775 + -0.5 x = 0.806225775 + -0.5 Combine like terms: 0.806225775 + -0.5 = 0.306225775 x = 0.306225775 Simplifying x = 0.306225775

Subproblem 2

x + 0.5 = -0.806225775 Simplifying x + 0.5 = -0.806225775 Reorder the terms: 0.5 + x = -0.806225775 Solving 0.5 + x = -0.806225775 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -0.806225775 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -0.806225775 + -0.5 x = -0.806225775 + -0.5 Combine like terms: -0.806225775 + -0.5 = -1.306225775 x = -1.306225775 Simplifying x = -1.306225775

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.306225775, -1.306225775}

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