(y+2)(y+2)-63=0

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Solution for (y+2)(y+2)-63=0 equation:


Simplifying
(y + 2)(y + 2) + -63 = 0

Reorder the terms:
(2 + y)(y + 2) + -63 = 0

Reorder the terms:
(2 + y)(2 + y) + -63 = 0

Multiply (2 + y) * (2 + y)
(2(2 + y) + y(2 + y)) + -63 = 0
((2 * 2 + y * 2) + y(2 + y)) + -63 = 0
((4 + 2y) + y(2 + y)) + -63 = 0
(4 + 2y + (2 * y + y * y)) + -63 = 0
(4 + 2y + (2y + y2)) + -63 = 0

Combine like terms: 2y + 2y = 4y
(4 + 4y + y2) + -63 = 0

Reorder the terms:
4 + -63 + 4y + y2 = 0

Combine like terms: 4 + -63 = -59
-59 + 4y + y2 = 0

Solving
-59 + 4y + y2 = 0

Solving for variable 'y'.

Begin completing the square.

Move the constant term to the right:

Add '59' to each side of the equation.
-59 + 4y + 59 + y2 = 0 + 59

Reorder the terms:
-59 + 59 + 4y + y2 = 0 + 59

Combine like terms: -59 + 59 = 0
0 + 4y + y2 = 0 + 59
4y + y2 = 0 + 59

Combine like terms: 0 + 59 = 59
4y + y2 = 59

The y term is 4y.  Take half its coefficient (2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
4y + 4 + y2 = 59 + 4

Reorder the terms:
4 + 4y + y2 = 59 + 4

Combine like terms: 59 + 4 = 63
4 + 4y + y2 = 63

Factor a perfect square on the left side:
(y + 2)(y + 2) = 63

Calculate the square root of the right side: 7.937253933

Break this problem into two subproblems by setting 
(y + 2) equal to 7.937253933 and -7.937253933.

Subproblem 1

y + 2 = 7.937253933 Simplifying y + 2 = 7.937253933 Reorder the terms: 2 + y = 7.937253933 Solving 2 + y = 7.937253933 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + y = 7.937253933 + -2 Combine like terms: 2 + -2 = 0 0 + y = 7.937253933 + -2 y = 7.937253933 + -2 Combine like terms: 7.937253933 + -2 = 5.937253933 y = 5.937253933 Simplifying y = 5.937253933

Subproblem 2

y + 2 = -7.937253933 Simplifying y + 2 = -7.937253933 Reorder the terms: 2 + y = -7.937253933 Solving 2 + y = -7.937253933 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + y = -7.937253933 + -2 Combine like terms: 2 + -2 = 0 0 + y = -7.937253933 + -2 y = -7.937253933 + -2 Combine like terms: -7.937253933 + -2 = -9.937253933 y = -9.937253933 Simplifying y = -9.937253933

Solution

The solution to the problem is based on the solutions from the subproblems. y = {5.937253933, -9.937253933}

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