2y^2+8y-10=-5

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Solution for 2y^2+8y-10=-5 equation:


Simplifying
2y2 + 8y + -10 = -5

Reorder the terms:
-10 + 8y + 2y2 = -5

Solving
-10 + 8y + 2y2 = -5

Solving for variable 'y'.

Reorder the terms:
-10 + 5 + 8y + 2y2 = -5 + 5

Combine like terms: -10 + 5 = -5
-5 + 8y + 2y2 = -5 + 5

Combine like terms: -5 + 5 = 0
-5 + 8y + 2y2 = 0

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

Divide each side by '2'.
-2.5 + 4y + y2 = 0

Move the constant term to the right:

Add '2.5' to each side of the equation.
-2.5 + 4y + 2.5 + y2 = 0 + 2.5

Reorder the terms:
-2.5 + 2.5 + 4y + y2 = 0 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + 4y + y2 = 0 + 2.5
4y + y2 = 0 + 2.5

Combine like terms: 0 + 2.5 = 2.5
4y + y2 = 2.5

The y term is 4y.  Take half its coefficient (2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
4y + 4 + y2 = 2.5 + 4

Reorder the terms:
4 + 4y + y2 = 2.5 + 4

Combine like terms: 2.5 + 4 = 6.5
4 + 4y + y2 = 6.5

Factor a perfect square on the left side:
(y + 2)(y + 2) = 6.5

Calculate the square root of the right side: 2.549509757

Break this problem into two subproblems by setting 
(y + 2) equal to 2.549509757 and -2.549509757.

Subproblem 1

y + 2 = 2.549509757 Simplifying y + 2 = 2.549509757 Reorder the terms: 2 + y = 2.549509757 Solving 2 + y = 2.549509757 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + y = 2.549509757 + -2 Combine like terms: 2 + -2 = 0 0 + y = 2.549509757 + -2 y = 2.549509757 + -2 Combine like terms: 2.549509757 + -2 = 0.549509757 y = 0.549509757 Simplifying y = 0.549509757

Subproblem 2

y + 2 = -2.549509757 Simplifying y + 2 = -2.549509757 Reorder the terms: 2 + y = -2.549509757 Solving 2 + y = -2.549509757 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + y = -2.549509757 + -2 Combine like terms: 2 + -2 = 0 0 + y = -2.549509757 + -2 y = -2.549509757 + -2 Combine like terms: -2.549509757 + -2 = -4.549509757 y = -4.549509757 Simplifying y = -4.549509757

Solution

The solution to the problem is based on the solutions from the subproblems. y = {0.549509757, -4.549509757}

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