y^2-14y=-42

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Solution for y^2-14y=-42 equation: 


Simplifying
y2 + -14y = -42

Reorder the terms:
-14y + y2 = -42

Solving
-14y + y2 = -42

Solving for variable 'y'.

Reorder the terms:
42 + -14y + y2 = -42 + 42

Combine like terms: -42 + 42 = 0
42 + -14y + y2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-42' to each side of the equation.
42 + -14y + -42 + y2 = 0 + -42

Reorder the terms:
42 + -42 + -14y + y2 = 0 + -42

Combine like terms: 42 + -42 = 0
0 + -14y + y2 = 0 + -42
-14y + y2 = 0 + -42

Combine like terms: 0 + -42 = -42
-14y + y2 = -42

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 = -42 + 49

Reorder the terms:
49 + -14y + y2 = -42 + 49

Combine like terms: -42 + 49 = 7
49 + -14y + y2 = 7

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

Calculate the square root of the right side: 2.645751311

Break this problem into two subproblems by setting 
(y + -7) equal to 2.645751311 and -2.645751311.


Subproblem 1
y + -7 = 2.645751311

Simplifying
y + -7 = 2.645751311

Reorder the terms:
-7 + y = 2.645751311

Solving
-7 + y = 2.645751311

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 = 2.645751311 + 7

Combine like terms: -7 + 7 = 0
0 + y = 2.645751311 + 7
y = 2.645751311 + 7

Combine like terms: 2.645751311 + 7 = 9.645751311
y = 9.645751311

Simplifying
y = 9.645751311


Subproblem 2
y + -7 = -2.645751311

Simplifying
y + -7 = -2.645751311

Reorder the terms:
-7 + y = -2.645751311

Solving
-7 + y = -2.645751311

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 = -2.645751311 + 7

Combine like terms: -7 + 7 = 0
0 + y = -2.645751311 + 7
y = -2.645751311 + 7

Combine like terms: -2.645751311 + 7 = 4.354248689
y = 4.354248689

Simplifying
y = 4.354248689


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {9.645751311, 4.354248689}

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