y^2+8y-3=0

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Solution for y^2+8y-3=0 equation:


Simplifying
y2 + 8y + -3 = 0

Reorder the terms:
-3 + 8y + y2 = 0

Solving
-3 + 8y + y2 = 0

Solving for variable 'y'.

Begin completing the square.

Move the constant term to the right:

Add '3' to each side of the equation.
-3 + 8y + 3 + y2 = 0 + 3

Reorder the terms:
-3 + 3 + 8y + y2 = 0 + 3

Combine like terms: -3 + 3 = 0
0 + 8y + y2 = 0 + 3
8y + y2 = 0 + 3

Combine like terms: 0 + 3 = 3
8y + y2 = 3

The y term is 8y.  Take half its coefficient (4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
8y + 16 + y2 = 3 + 16

Reorder the terms:
16 + 8y + y2 = 3 + 16

Combine like terms: 3 + 16 = 19
16 + 8y + y2 = 19

Factor a perfect square on the left side:
(y + 4)(y + 4) = 19

Calculate the square root of the right side: 4.358898944

Break this problem into two subproblems by setting 
(y + 4) equal to 4.358898944 and -4.358898944.

Subproblem 1

y + 4 = 4.358898944 Simplifying y + 4 = 4.358898944 Reorder the terms: 4 + y = 4.358898944 Solving 4 + y = 4.358898944 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + y = 4.358898944 + -4 Combine like terms: 4 + -4 = 0 0 + y = 4.358898944 + -4 y = 4.358898944 + -4 Combine like terms: 4.358898944 + -4 = 0.358898944 y = 0.358898944 Simplifying y = 0.358898944

Subproblem 2

y + 4 = -4.358898944 Simplifying y + 4 = -4.358898944 Reorder the terms: 4 + y = -4.358898944 Solving 4 + y = -4.358898944 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + y = -4.358898944 + -4 Combine like terms: 4 + -4 = 0 0 + y = -4.358898944 + -4 y = -4.358898944 + -4 Combine like terms: -4.358898944 + -4 = -8.358898944 y = -8.358898944 Simplifying y = -8.358898944

Solution

The solution to the problem is based on the solutions from the subproblems. y = {0.358898944, -8.358898944}

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