y^2-14y=-32

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Solution for y^2-14y=-32 equation:


Simplifying
y2 + -14y = -32

Reorder the terms:
-14y + y2 = -32

Solving
-14y + y2 = -32

Solving for variable 'y'.

Reorder the terms:
32 + -14y + y2 = -32 + 32

Combine like terms: -32 + 32 = 0
32 + -14y + y2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-32' to each side of the equation.
32 + -14y + -32 + y2 = 0 + -32

Reorder the terms:
32 + -32 + -14y + y2 = 0 + -32

Combine like terms: 32 + -32 = 0
0 + -14y + y2 = 0 + -32
-14y + y2 = 0 + -32

Combine like terms: 0 + -32 = -32
-14y + y2 = -32

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 = -32 + 49

Reorder the terms:
49 + -14y + y2 = -32 + 49

Combine like terms: -32 + 49 = 17
49 + -14y + y2 = 17

Factor a perfect square on the left side:
(y + -7)(y + -7) = 17

Calculate the square root of the right side: 4.123105626

Break this problem into two subproblems by setting 
(y + -7) equal to 4.123105626 and -4.123105626.

Subproblem 1

y + -7 = 4.123105626 Simplifying y + -7 = 4.123105626 Reorder the terms: -7 + y = 4.123105626 Solving -7 + y = 4.123105626 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 = 4.123105626 + 7 Combine like terms: -7 + 7 = 0 0 + y = 4.123105626 + 7 y = 4.123105626 + 7 Combine like terms: 4.123105626 + 7 = 11.123105626 y = 11.123105626 Simplifying y = 11.123105626

Subproblem 2

y + -7 = -4.123105626 Simplifying y + -7 = -4.123105626 Reorder the terms: -7 + y = -4.123105626 Solving -7 + y = -4.123105626 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 = -4.123105626 + 7 Combine like terms: -7 + 7 = 0 0 + y = -4.123105626 + 7 y = -4.123105626 + 7 Combine like terms: -4.123105626 + 7 = 2.876894374 y = 2.876894374 Simplifying y = 2.876894374

Solution

The solution to the problem is based on the solutions from the subproblems. y = {11.123105626, 2.876894374}

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