y^2-2y-120=27

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Solution for y^2-2y-120=27 equation:


Simplifying
y2 + -2y + -120 = 27

Reorder the terms:
-120 + -2y + y2 = 27

Solving
-120 + -2y + y2 = 27

Solving for variable 'y'.

Reorder the terms:
-120 + -27 + -2y + y2 = 27 + -27

Combine like terms: -120 + -27 = -147
-147 + -2y + y2 = 27 + -27

Combine like terms: 27 + -27 = 0
-147 + -2y + y2 = 0

Begin completing the square.

Move the constant term to the right:

Add '147' to each side of the equation.
-147 + -2y + 147 + y2 = 0 + 147

Reorder the terms:
-147 + 147 + -2y + y2 = 0 + 147

Combine like terms: -147 + 147 = 0
0 + -2y + y2 = 0 + 147
-2y + y2 = 0 + 147

Combine like terms: 0 + 147 = 147
-2y + y2 = 147

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 = 147 + 1

Reorder the terms:
1 + -2y + y2 = 147 + 1

Combine like terms: 147 + 1 = 148
1 + -2y + y2 = 148

Factor a perfect square on the left side:
(y + -1)(y + -1) = 148

Calculate the square root of the right side: 12.165525061

Break this problem into two subproblems by setting 
(y + -1) equal to 12.165525061 and -12.165525061.

Subproblem 1

y + -1 = 12.165525061 Simplifying y + -1 = 12.165525061 Reorder the terms: -1 + y = 12.165525061 Solving -1 + y = 12.165525061 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 = 12.165525061 + 1 Combine like terms: -1 + 1 = 0 0 + y = 12.165525061 + 1 y = 12.165525061 + 1 Combine like terms: 12.165525061 + 1 = 13.165525061 y = 13.165525061 Simplifying y = 13.165525061

Subproblem 2

y + -1 = -12.165525061 Simplifying y + -1 = -12.165525061 Reorder the terms: -1 + y = -12.165525061 Solving -1 + y = -12.165525061 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 = -12.165525061 + 1 Combine like terms: -1 + 1 = 0 0 + y = -12.165525061 + 1 y = -12.165525061 + 1 Combine like terms: -12.165525061 + 1 = -11.165525061 y = -11.165525061 Simplifying y = -11.165525061

Solution

The solution to the problem is based on the solutions from the subproblems. y = {13.165525061, -11.165525061}

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