y^2+2y-90=0

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Solution for y^2+2y-90=0 equation:


Simplifying
y2 + 2y + -90 = 0

Reorder the terms:
-90 + 2y + y2 = 0

Solving
-90 + 2y + y2 = 0

Solving for variable 'y'.

Begin completing the square.

Move the constant term to the right:

Add '90' to each side of the equation.
-90 + 2y + 90 + y2 = 0 + 90

Reorder the terms:
-90 + 90 + 2y + y2 = 0 + 90

Combine like terms: -90 + 90 = 0
0 + 2y + y2 = 0 + 90
2y + y2 = 0 + 90

Combine like terms: 0 + 90 = 90
2y + y2 = 90

The y term is 2y.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2y + 1 + y2 = 90 + 1

Reorder the terms:
1 + 2y + y2 = 90 + 1

Combine like terms: 90 + 1 = 91
1 + 2y + y2 = 91

Factor a perfect square on the left side:
(y + 1)(y + 1) = 91

Calculate the square root of the right side: 9.539392014

Break this problem into two subproblems by setting 
(y + 1) equal to 9.539392014 and -9.539392014.

Subproblem 1

y + 1 = 9.539392014 Simplifying y + 1 = 9.539392014 Reorder the terms: 1 + y = 9.539392014 Solving 1 + y = 9.539392014 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + y = 9.539392014 + -1 Combine like terms: 1 + -1 = 0 0 + y = 9.539392014 + -1 y = 9.539392014 + -1 Combine like terms: 9.539392014 + -1 = 8.539392014 y = 8.539392014 Simplifying y = 8.539392014

Subproblem 2

y + 1 = -9.539392014 Simplifying y + 1 = -9.539392014 Reorder the terms: 1 + y = -9.539392014 Solving 1 + y = -9.539392014 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + y = -9.539392014 + -1 Combine like terms: 1 + -1 = 0 0 + y = -9.539392014 + -1 y = -9.539392014 + -1 Combine like terms: -9.539392014 + -1 = -10.539392014 y = -10.539392014 Simplifying y = -10.539392014

Solution

The solution to the problem is based on the solutions from the subproblems. y = {8.539392014, -10.539392014}

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