y^2-24y-70=0

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Solution for y^2-24y-70=0 equation: 


Simplifying
y2 + -24y + -70 = 0

Reorder the terms:
-70 + -24y + y2 = 0

Solving
-70 + -24y + y2 = 0

Solving for variable 'y'.

Begin completing the square.

Move the constant term to the right:

Add '70' to each side of the equation.
-70 + -24y + 70 + y2 = 0 + 70

Reorder the terms:
-70 + 70 + -24y + y2 = 0 + 70

Combine like terms: -70 + 70 = 0
0 + -24y + y2 = 0 + 70
-24y + y2 = 0 + 70

Combine like terms: 0 + 70 = 70
-24y + y2 = 70

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 = 70 + 144

Reorder the terms:
144 + -24y + y2 = 70 + 144

Combine like terms: 70 + 144 = 214
144 + -24y + y2 = 214

Factor a perfect square on the left side:
(y + -12)(y + -12) = 214

Calculate the square root of the right side: 14.628738838

Break this problem into two subproblems by setting 
(y + -12) equal to 14.628738838 and -14.628738838.


Subproblem 1
y + -12 = 14.628738838

Simplifying
y + -12 = 14.628738838

Reorder the terms:
-12 + y = 14.628738838

Solving
-12 + y = 14.628738838

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 = 14.628738838 + 12

Combine like terms: -12 + 12 = 0
0 + y = 14.628738838 + 12
y = 14.628738838 + 12

Combine like terms: 14.628738838 + 12 = 26.628738838
y = 26.628738838

Simplifying
y = 26.628738838


Subproblem 2
y + -12 = -14.628738838

Simplifying
y + -12 = -14.628738838

Reorder the terms:
-12 + y = -14.628738838

Solving
-12 + y = -14.628738838

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 = -14.628738838 + 12

Combine like terms: -12 + 12 = 0
0 + y = -14.628738838 + 12
y = -14.628738838 + 12

Combine like terms: -14.628738838 + 12 = -2.628738838
y = -2.628738838

Simplifying
y = -2.628738838


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {26.628738838, -2.628738838}

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