y^2+6y-15=0

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Solution for y^2+6y-15=0 equation:


Simplifying
y2 + 6y + -15 = 0

Reorder the terms:
-15 + 6y + y2 = 0

Solving
-15 + 6y + y2 = 0

Solving for variable 'y'.

Begin completing the square.

Move the constant term to the right:

Add '15' to each side of the equation.
-15 + 6y + 15 + y2 = 0 + 15

Reorder the terms:
-15 + 15 + 6y + y2 = 0 + 15

Combine like terms: -15 + 15 = 0
0 + 6y + y2 = 0 + 15
6y + y2 = 0 + 15

Combine like terms: 0 + 15 = 15
6y + y2 = 15

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 = 15 + 9

Reorder the terms:
9 + 6y + y2 = 15 + 9

Combine like terms: 15 + 9 = 24
9 + 6y + y2 = 24

Factor a perfect square on the left side:
(y + 3)(y + 3) = 24

Calculate the square root of the right side: 4.898979486

Break this problem into two subproblems by setting 
(y + 3) equal to 4.898979486 and -4.898979486.

Subproblem 1

y + 3 = 4.898979486 Simplifying y + 3 = 4.898979486 Reorder the terms: 3 + y = 4.898979486 Solving 3 + y = 4.898979486 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + y = 4.898979486 + -3 Combine like terms: 3 + -3 = 0 0 + y = 4.898979486 + -3 y = 4.898979486 + -3 Combine like terms: 4.898979486 + -3 = 1.898979486 y = 1.898979486 Simplifying y = 1.898979486

Subproblem 2

y + 3 = -4.898979486 Simplifying y + 3 = -4.898979486 Reorder the terms: 3 + y = -4.898979486 Solving 3 + y = -4.898979486 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + y = -4.898979486 + -3 Combine like terms: 3 + -3 = 0 0 + y = -4.898979486 + -3 y = -4.898979486 + -3 Combine like terms: -4.898979486 + -3 = -7.898979486 y = -7.898979486 Simplifying y = -7.898979486

Solution

The solution to the problem is based on the solutions from the subproblems. y = {1.898979486, -7.898979486}

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