y^2-24y-27=0

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Solution for y^2-24y-27=0 equation:


Simplifying
y2 + -24y + -27 = 0

Reorder the terms:
-27 + -24y + y2 = 0

Solving
-27 + -24y + y2 = 0

Solving for variable 'y'.

Begin completing the square.

Move the constant term to the right:

Add '27' to each side of the equation.
-27 + -24y + 27 + y2 = 0 + 27

Reorder the terms:
-27 + 27 + -24y + y2 = 0 + 27

Combine like terms: -27 + 27 = 0
0 + -24y + y2 = 0 + 27
-24y + y2 = 0 + 27

Combine like terms: 0 + 27 = 27
-24y + y2 = 27

The y term is -24y.  Take half its coefficient (-12).
Square it (144) and add it to both sides.

Add '144' to each side of the equation.
-24y + 144 + y2 = 27 + 144

Reorder the terms:
144 + -24y + y2 = 27 + 144

Combine like terms: 27 + 144 = 171
144 + -24y + y2 = 171

Factor a perfect square on the left side:
(y + -12)(y + -12) = 171

Calculate the square root of the right side: 13.076696831

Break this problem into two subproblems by setting 
(y + -12) equal to 13.076696831 and -13.076696831.

Subproblem 1

y + -12 = 13.076696831 Simplifying y + -12 = 13.076696831 Reorder the terms: -12 + y = 13.076696831 Solving -12 + y = 13.076696831 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + y = 13.076696831 + 12 Combine like terms: -12 + 12 = 0 0 + y = 13.076696831 + 12 y = 13.076696831 + 12 Combine like terms: 13.076696831 + 12 = 25.076696831 y = 25.076696831 Simplifying y = 25.076696831

Subproblem 2

y + -12 = -13.076696831 Simplifying y + -12 = -13.076696831 Reorder the terms: -12 + y = -13.076696831 Solving -12 + y = -13.076696831 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + y = -13.076696831 + 12 Combine like terms: -12 + 12 = 0 0 + y = -13.076696831 + 12 y = -13.076696831 + 12 Combine like terms: -13.076696831 + 12 = -1.076696831 y = -1.076696831 Simplifying y = -1.076696831

Solution

The solution to the problem is based on the solutions from the subproblems. y = {25.076696831, -1.076696831}

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