y^2-14y-30=0

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Solution for y^2-14y-30=0 equation:


Simplifying
y2 + -14y + -30 = 0

Reorder the terms:
-30 + -14y + y2 = 0

Solving
-30 + -14y + y2 = 0

Solving for variable 'y'.

Begin completing the square.

Move the constant term to the right:

Add '30' to each side of the equation.
-30 + -14y + 30 + y2 = 0 + 30

Reorder the terms:
-30 + 30 + -14y + y2 = 0 + 30

Combine like terms: -30 + 30 = 0
0 + -14y + y2 = 0 + 30
-14y + y2 = 0 + 30

Combine like terms: 0 + 30 = 30
-14y + y2 = 30

The y term is -14y.  Take half its coefficient (-7).
Square it (49) and add it to both sides.

Add '49' to each side of the equation.
-14y + 49 + y2 = 30 + 49

Reorder the terms:
49 + -14y + y2 = 30 + 49

Combine like terms: 30 + 49 = 79
49 + -14y + y2 = 79

Factor a perfect square on the left side:
(y + -7)(y + -7) = 79

Calculate the square root of the right side: 8.888194417

Break this problem into two subproblems by setting 
(y + -7) equal to 8.888194417 and -8.888194417.

Subproblem 1

y + -7 = 8.888194417 Simplifying y + -7 = 8.888194417 Reorder the terms: -7 + y = 8.888194417 Solving -7 + y = 8.888194417 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + y = 8.888194417 + 7 Combine like terms: -7 + 7 = 0 0 + y = 8.888194417 + 7 y = 8.888194417 + 7 Combine like terms: 8.888194417 + 7 = 15.888194417 y = 15.888194417 Simplifying y = 15.888194417

Subproblem 2

y + -7 = -8.888194417 Simplifying y + -7 = -8.888194417 Reorder the terms: -7 + y = -8.888194417 Solving -7 + y = -8.888194417 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + y = -8.888194417 + 7 Combine like terms: -7 + 7 = 0 0 + y = -8.888194417 + 7 y = -8.888194417 + 7 Combine like terms: -8.888194417 + 7 = -1.888194417 y = -1.888194417 Simplifying y = -1.888194417

Solution

The solution to the problem is based on the solutions from the subproblems. y = {15.888194417, -1.888194417}

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