(y-2)*(y+2)=2y^2+6y+25

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Solution for (y-2)*(y+2)=2y^2+6y+25 equation:


Simplifying
(y + -2)(y + 2) = 2y2 + 6y + 25

Reorder the terms:
(-2 + y)(y + 2) = 2y2 + 6y + 25

Reorder the terms:
(-2 + y)(2 + y) = 2y2 + 6y + 25

Multiply (-2 + y) * (2 + y)
(-2(2 + y) + y(2 + y)) = 2y2 + 6y + 25
((2 * -2 + y * -2) + y(2 + y)) = 2y2 + 6y + 25
((-4 + -2y) + y(2 + y)) = 2y2 + 6y + 25
(-4 + -2y + (2 * y + y * y)) = 2y2 + 6y + 25
(-4 + -2y + (2y + y2)) = 2y2 + 6y + 25

Combine like terms: -2y + 2y = 0
(-4 + 0 + y2) = 2y2 + 6y + 25
(-4 + y2) = 2y2 + 6y + 25

Reorder the terms:
-4 + y2 = 25 + 6y + 2y2

Solving
-4 + y2 = 25 + 6y + 2y2

Solving for variable 'y'.

Reorder the terms:
-4 + -25 + -6y + y2 + -2y2 = 25 + 6y + 2y2 + -25 + -6y + -2y2

Combine like terms: -4 + -25 = -29
-29 + -6y + y2 + -2y2 = 25 + 6y + 2y2 + -25 + -6y + -2y2

Combine like terms: y2 + -2y2 = -1y2
-29 + -6y + -1y2 = 25 + 6y + 2y2 + -25 + -6y + -2y2

Reorder the terms:
-29 + -6y + -1y2 = 25 + -25 + 6y + -6y + 2y2 + -2y2

Combine like terms: 25 + -25 = 0
-29 + -6y + -1y2 = 0 + 6y + -6y + 2y2 + -2y2
-29 + -6y + -1y2 = 6y + -6y + 2y2 + -2y2

Combine like terms: 6y + -6y = 0
-29 + -6y + -1y2 = 0 + 2y2 + -2y2
-29 + -6y + -1y2 = 2y2 + -2y2

Combine like terms: 2y2 + -2y2 = 0
-29 + -6y + -1y2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(29 + 6y + y2) = 0

Ignore the factor -1.

Subproblem 1

Set the factor '(29 + 6y + y2)' equal to zero and attempt to solve: Simplifying 29 + 6y + y2 = 0 Solving 29 + 6y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '-29' to each side of the equation. 29 + 6y + -29 + y2 = 0 + -29 Reorder the terms: 29 + -29 + 6y + y2 = 0 + -29 Combine like terms: 29 + -29 = 0 0 + 6y + y2 = 0 + -29 6y + y2 = 0 + -29 Combine like terms: 0 + -29 = -29 6y + y2 = -29 The y term is 6y. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6y + 9 + y2 = -29 + 9 Reorder the terms: 9 + 6y + y2 = -29 + 9 Combine like terms: -29 + 9 = -20 9 + 6y + y2 = -20 Factor a perfect square on the left side: (y + 3)(y + 3) = -20 Can't calculate square root of the right side. The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.

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