y^2-12y-14=0

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Solution for y^2-12y-14=0 equation:


Simplifying
y2 + -12y + -14 = 0

Reorder the terms:
-14 + -12y + y2 = 0

Solving
-14 + -12y + y2 = 0

Solving for variable 'y'.

Begin completing the square.

Move the constant term to the right:

Add '14' to each side of the equation.
-14 + -12y + 14 + y2 = 0 + 14

Reorder the terms:
-14 + 14 + -12y + y2 = 0 + 14

Combine like terms: -14 + 14 = 0
0 + -12y + y2 = 0 + 14
-12y + y2 = 0 + 14

Combine like terms: 0 + 14 = 14
-12y + y2 = 14

The y term is -12y.  Take half its coefficient (-6).
Square it (36) and add it to both sides.

Add '36' to each side of the equation.
-12y + 36 + y2 = 14 + 36

Reorder the terms:
36 + -12y + y2 = 14 + 36

Combine like terms: 14 + 36 = 50
36 + -12y + y2 = 50

Factor a perfect square on the left side:
(y + -6)(y + -6) = 50

Calculate the square root of the right side: 7.071067812

Break this problem into two subproblems by setting 
(y + -6) equal to 7.071067812 and -7.071067812.

Subproblem 1

y + -6 = 7.071067812 Simplifying y + -6 = 7.071067812 Reorder the terms: -6 + y = 7.071067812 Solving -6 + y = 7.071067812 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + y = 7.071067812 + 6 Combine like terms: -6 + 6 = 0 0 + y = 7.071067812 + 6 y = 7.071067812 + 6 Combine like terms: 7.071067812 + 6 = 13.071067812 y = 13.071067812 Simplifying y = 13.071067812

Subproblem 2

y + -6 = -7.071067812 Simplifying y + -6 = -7.071067812 Reorder the terms: -6 + y = -7.071067812 Solving -6 + y = -7.071067812 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + y = -7.071067812 + 6 Combine like terms: -6 + 6 = 0 0 + y = -7.071067812 + 6 y = -7.071067812 + 6 Combine like terms: -7.071067812 + 6 = -1.071067812 y = -1.071067812 Simplifying y = -1.071067812

Solution

The solution to the problem is based on the solutions from the subproblems. y = {13.071067812, -1.071067812}

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