(y+3)y=14

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Solution for (y+3)y=14 equation:


Simplifying
(y + 3) * y = 14

Reorder the terms:
(3 + y) * y = 14

Reorder the terms for easier multiplication:
y(3 + y) = 14
(3 * y + y * y) = 14
(3y + y2) = 14

Solving
3y + y2 = 14

Solving for variable 'y'.

Reorder the terms:
-14 + 3y + y2 = 14 + -14

Combine like terms: 14 + -14 = 0
-14 + 3y + y2 = 0

Begin completing the square.

Move the constant term to the right:

Add '14' to each side of the equation.
-14 + 3y + 14 + y2 = 0 + 14

Reorder the terms:
-14 + 14 + 3y + y2 = 0 + 14

Combine like terms: -14 + 14 = 0
0 + 3y + y2 = 0 + 14
3y + y2 = 0 + 14

Combine like terms: 0 + 14 = 14
3y + y2 = 14

The y term is 3y.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3y + 2.25 + y2 = 14 + 2.25

Reorder the terms:
2.25 + 3y + y2 = 14 + 2.25

Combine like terms: 14 + 2.25 = 16.25
2.25 + 3y + y2 = 16.25

Factor a perfect square on the left side:
(y + 1.5)(y + 1.5) = 16.25

Calculate the square root of the right side: 4.031128874

Break this problem into two subproblems by setting 
(y + 1.5) equal to 4.031128874 and -4.031128874.

Subproblem 1

y + 1.5 = 4.031128874 Simplifying y + 1.5 = 4.031128874 Reorder the terms: 1.5 + y = 4.031128874 Solving 1.5 + y = 4.031128874 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + y = 4.031128874 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + y = 4.031128874 + -1.5 y = 4.031128874 + -1.5 Combine like terms: 4.031128874 + -1.5 = 2.531128874 y = 2.531128874 Simplifying y = 2.531128874

Subproblem 2

y + 1.5 = -4.031128874 Simplifying y + 1.5 = -4.031128874 Reorder the terms: 1.5 + y = -4.031128874 Solving 1.5 + y = -4.031128874 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + y = -4.031128874 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + y = -4.031128874 + -1.5 y = -4.031128874 + -1.5 Combine like terms: -4.031128874 + -1.5 = -5.531128874 y = -5.531128874 Simplifying y = -5.531128874

Solution

The solution to the problem is based on the solutions from the subproblems. y = {2.531128874, -5.531128874}

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