y^2+14=8y

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Solution for y^2+14=8y equation:


Simplifying
y2 + 14 = 8y

Reorder the terms:
14 + y2 = 8y

Solving
14 + y2 = 8y

Solving for variable 'y'.

Reorder the terms:
14 + -8y + y2 = 8y + -8y

Combine like terms: 8y + -8y = 0
14 + -8y + y2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-14' to each side of the equation.
14 + -8y + -14 + y2 = 0 + -14

Reorder the terms:
14 + -14 + -8y + y2 = 0 + -14

Combine like terms: 14 + -14 = 0
0 + -8y + y2 = 0 + -14
-8y + y2 = 0 + -14

Combine like terms: 0 + -14 = -14
-8y + y2 = -14

The y term is -8y.  Take half its coefficient (-4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
-8y + 16 + y2 = -14 + 16

Reorder the terms:
16 + -8y + y2 = -14 + 16

Combine like terms: -14 + 16 = 2
16 + -8y + y2 = 2

Factor a perfect square on the left side:
(y + -4)(y + -4) = 2

Calculate the square root of the right side: 1.414213562

Break this problem into two subproblems by setting 
(y + -4) equal to 1.414213562 and -1.414213562.

Subproblem 1

y + -4 = 1.414213562 Simplifying y + -4 = 1.414213562 Reorder the terms: -4 + y = 1.414213562 Solving -4 + y = 1.414213562 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + y = 1.414213562 + 4 Combine like terms: -4 + 4 = 0 0 + y = 1.414213562 + 4 y = 1.414213562 + 4 Combine like terms: 1.414213562 + 4 = 5.414213562 y = 5.414213562 Simplifying y = 5.414213562

Subproblem 2

y + -4 = -1.414213562 Simplifying y + -4 = -1.414213562 Reorder the terms: -4 + y = -1.414213562 Solving -4 + y = -1.414213562 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + y = -1.414213562 + 4 Combine like terms: -4 + 4 = 0 0 + y = -1.414213562 + 4 y = -1.414213562 + 4 Combine like terms: -1.414213562 + 4 = 2.585786438 y = 2.585786438 Simplifying y = 2.585786438

Solution

The solution to the problem is based on the solutions from the subproblems. y = {5.414213562, 2.585786438}

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