y^2+26y=-47

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Solution for y^2+26y=-47 equation:


Simplifying
y2 + 26y = -47

Reorder the terms:
26y + y2 = -47

Solving
26y + y2 = -47

Solving for variable 'y'.

Reorder the terms:
47 + 26y + y2 = -47 + 47

Combine like terms: -47 + 47 = 0
47 + 26y + y2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-47' to each side of the equation.
47 + 26y + -47 + y2 = 0 + -47

Reorder the terms:
47 + -47 + 26y + y2 = 0 + -47

Combine like terms: 47 + -47 = 0
0 + 26y + y2 = 0 + -47
26y + y2 = 0 + -47

Combine like terms: 0 + -47 = -47
26y + y2 = -47

The y term is 26y.  Take half its coefficient (13).
Square it (169) and add it to both sides.

Add '169' to each side of the equation.
26y + 169 + y2 = -47 + 169

Reorder the terms:
169 + 26y + y2 = -47 + 169

Combine like terms: -47 + 169 = 122
169 + 26y + y2 = 122

Factor a perfect square on the left side:
(y + 13)(y + 13) = 122

Calculate the square root of the right side: 11.045361017

Break this problem into two subproblems by setting 
(y + 13) equal to 11.045361017 and -11.045361017.

Subproblem 1

y + 13 = 11.045361017 Simplifying y + 13 = 11.045361017 Reorder the terms: 13 + y = 11.045361017 Solving 13 + y = 11.045361017 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-13' to each side of the equation. 13 + -13 + y = 11.045361017 + -13 Combine like terms: 13 + -13 = 0 0 + y = 11.045361017 + -13 y = 11.045361017 + -13 Combine like terms: 11.045361017 + -13 = -1.954638983 y = -1.954638983 Simplifying y = -1.954638983

Subproblem 2

y + 13 = -11.045361017 Simplifying y + 13 = -11.045361017 Reorder the terms: 13 + y = -11.045361017 Solving 13 + y = -11.045361017 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-13' to each side of the equation. 13 + -13 + y = -11.045361017 + -13 Combine like terms: 13 + -13 = 0 0 + y = -11.045361017 + -13 y = -11.045361017 + -13 Combine like terms: -11.045361017 + -13 = -24.045361017 y = -24.045361017 Simplifying y = -24.045361017

Solution

The solution to the problem is based on the solutions from the subproblems. y = {-1.954638983, -24.045361017}

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