(y-4)(y-4)=18

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Solution for (y-4)(y-4)=18 equation:


Simplifying
(y + -4)(y + -4) = 18

Reorder the terms:
(-4 + y)(y + -4) = 18

Reorder the terms:
(-4 + y)(-4 + y) = 18

Multiply (-4 + y) * (-4 + y)
(-4(-4 + y) + y(-4 + y)) = 18
((-4 * -4 + y * -4) + y(-4 + y)) = 18
((16 + -4y) + y(-4 + y)) = 18
(16 + -4y + (-4 * y + y * y)) = 18
(16 + -4y + (-4y + y2)) = 18

Combine like terms: -4y + -4y = -8y
(16 + -8y + y2) = 18

Solving
16 + -8y + y2 = 18

Solving for variable 'y'.

Reorder the terms:
16 + -18 + -8y + y2 = 18 + -18

Combine like terms: 16 + -18 = -2
-2 + -8y + y2 = 18 + -18

Combine like terms: 18 + -18 = 0
-2 + -8y + y2 = 0

Begin completing the square.

Move the constant term to the right:

Add '2' to each side of the equation.
-2 + -8y + 2 + y2 = 0 + 2

Reorder the terms:
-2 + 2 + -8y + y2 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -8y + y2 = 0 + 2
-8y + y2 = 0 + 2

Combine like terms: 0 + 2 = 2
-8y + y2 = 2

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 = 2 + 16

Reorder the terms:
16 + -8y + y2 = 2 + 16

Combine like terms: 2 + 16 = 18
16 + -8y + y2 = 18

Factor a perfect square on the left side:
(y + -4)(y + -4) = 18

Calculate the square root of the right side: 4.242640687

Break this problem into two subproblems by setting 
(y + -4) equal to 4.242640687 and -4.242640687.

Subproblem 1

y + -4 = 4.242640687 Simplifying y + -4 = 4.242640687 Reorder the terms: -4 + y = 4.242640687 Solving -4 + y = 4.242640687 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 = 4.242640687 + 4 Combine like terms: -4 + 4 = 0 0 + y = 4.242640687 + 4 y = 4.242640687 + 4 Combine like terms: 4.242640687 + 4 = 8.242640687 y = 8.242640687 Simplifying y = 8.242640687

Subproblem 2

y + -4 = -4.242640687 Simplifying y + -4 = -4.242640687 Reorder the terms: -4 + y = -4.242640687 Solving -4 + y = -4.242640687 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 = -4.242640687 + 4 Combine like terms: -4 + 4 = 0 0 + y = -4.242640687 + 4 y = -4.242640687 + 4 Combine like terms: -4.242640687 + 4 = -0.242640687 y = -0.242640687 Simplifying y = -0.242640687

Solution

The solution to the problem is based on the solutions from the subproblems. y = {8.242640687, -0.242640687}

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