y^2+7y+14=7

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Solution for y^2+7y+14=7 equation:


Simplifying
y2 + 7y + 14 = 7

Reorder the terms:
14 + 7y + y2 = 7

Solving
14 + 7y + y2 = 7

Solving for variable 'y'.

Reorder the terms:
14 + -7 + 7y + y2 = 7 + -7

Combine like terms: 14 + -7 = 7
7 + 7y + y2 = 7 + -7

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

Begin completing the square.

Move the constant term to the right:

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

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

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

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

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 = -7 + 12.25

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

Combine like terms: -7 + 12.25 = 5.25
12.25 + 7y + y2 = 5.25

Factor a perfect square on the left side:
(y + 3.5)(y + 3.5) = 5.25

Calculate the square root of the right side: 2.291287847

Break this problem into two subproblems by setting 
(y + 3.5) equal to 2.291287847 and -2.291287847.

Subproblem 1

y + 3.5 = 2.291287847 Simplifying y + 3.5 = 2.291287847 Reorder the terms: 3.5 + y = 2.291287847 Solving 3.5 + y = 2.291287847 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 = 2.291287847 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + y = 2.291287847 + -3.5 y = 2.291287847 + -3.5 Combine like terms: 2.291287847 + -3.5 = -1.208712153 y = -1.208712153 Simplifying y = -1.208712153

Subproblem 2

y + 3.5 = -2.291287847 Simplifying y + 3.5 = -2.291287847 Reorder the terms: 3.5 + y = -2.291287847 Solving 3.5 + y = -2.291287847 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 = -2.291287847 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + y = -2.291287847 + -3.5 y = -2.291287847 + -3.5 Combine like terms: -2.291287847 + -3.5 = -5.791287847 y = -5.791287847 Simplifying y = -5.791287847

Solution

The solution to the problem is based on the solutions from the subproblems. y = {-1.208712153, -5.791287847}

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