2y^2+14y=-19

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Solution for 2y^2+14y=-19 equation:


Simplifying
2y2 + 14y = -19

Reorder the terms:
14y + 2y2 = -19

Solving
14y + 2y2 = -19

Solving for variable 'y'.

Reorder the terms:
19 + 14y + 2y2 = -19 + 19

Combine like terms: -19 + 19 = 0
19 + 14y + 2y2 = 0

Begin completing the square.  Divide all terms by
2 the coefficient of the squared term: 

Divide each side by '2'.
9.5 + 7y + y2 = 0

Move the constant term to the right:

Add '-9.5' to each side of the equation.
9.5 + 7y + -9.5 + y2 = 0 + -9.5

Reorder the terms:
9.5 + -9.5 + 7y + y2 = 0 + -9.5

Combine like terms: 9.5 + -9.5 = 0.0
0.0 + 7y + y2 = 0 + -9.5
7y + y2 = 0 + -9.5

Combine like terms: 0 + -9.5 = -9.5
7y + y2 = -9.5

The y term is 7y.  Take half its coefficient (3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
7y + 12.25 + y2 = -9.5 + 12.25

Reorder the terms:
12.25 + 7y + y2 = -9.5 + 12.25

Combine like terms: -9.5 + 12.25 = 2.75
12.25 + 7y + y2 = 2.75

Factor a perfect square on the left side:
(y + 3.5)(y + 3.5) = 2.75

Calculate the square root of the right side: 1.658312395

Break this problem into two subproblems by setting 
(y + 3.5) equal to 1.658312395 and -1.658312395.

Subproblem 1

y + 3.5 = 1.658312395 Simplifying y + 3.5 = 1.658312395 Reorder the terms: 3.5 + y = 1.658312395 Solving 3.5 + y = 1.658312395 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + y = 1.658312395 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + y = 1.658312395 + -3.5 y = 1.658312395 + -3.5 Combine like terms: 1.658312395 + -3.5 = -1.841687605 y = -1.841687605 Simplifying y = -1.841687605

Subproblem 2

y + 3.5 = -1.658312395 Simplifying y + 3.5 = -1.658312395 Reorder the terms: 3.5 + y = -1.658312395 Solving 3.5 + y = -1.658312395 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + y = -1.658312395 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + y = -1.658312395 + -3.5 y = -1.658312395 + -3.5 Combine like terms: -1.658312395 + -3.5 = -5.158312395 y = -5.158312395 Simplifying y = -5.158312395

Solution

The solution to the problem is based on the solutions from the subproblems. y = {-1.841687605, -5.158312395}

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