5y^2+40y-4=0

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Solution for 5y^2+40y-4=0 equation:


Simplifying
5y2 + 40y + -4 = 0

Reorder the terms:
-4 + 40y + 5y2 = 0

Solving
-4 + 40y + 5y2 = 0

Solving for variable 'y'.

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

Divide each side by '5'.
-0.8 + 8y + y2 = 0

Move the constant term to the right:

Add '0.8' to each side of the equation.
-0.8 + 8y + 0.8 + y2 = 0 + 0.8

Reorder the terms:
-0.8 + 0.8 + 8y + y2 = 0 + 0.8

Combine like terms: -0.8 + 0.8 = 0.0
0.0 + 8y + y2 = 0 + 0.8
8y + y2 = 0 + 0.8

Combine like terms: 0 + 0.8 = 0.8
8y + y2 = 0.8

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 = 0.8 + 16

Reorder the terms:
16 + 8y + y2 = 0.8 + 16

Combine like terms: 0.8 + 16 = 16.8
16 + 8y + y2 = 16.8

Factor a perfect square on the left side:
(y + 4)(y + 4) = 16.8

Calculate the square root of the right side: 4.098780306

Break this problem into two subproblems by setting 
(y + 4) equal to 4.098780306 and -4.098780306.

Subproblem 1

y + 4 = 4.098780306 Simplifying y + 4 = 4.098780306 Reorder the terms: 4 + y = 4.098780306 Solving 4 + y = 4.098780306 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 = 4.098780306 + -4 Combine like terms: 4 + -4 = 0 0 + y = 4.098780306 + -4 y = 4.098780306 + -4 Combine like terms: 4.098780306 + -4 = 0.098780306 y = 0.098780306 Simplifying y = 0.098780306

Subproblem 2

y + 4 = -4.098780306 Simplifying y + 4 = -4.098780306 Reorder the terms: 4 + y = -4.098780306 Solving 4 + y = -4.098780306 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 = -4.098780306 + -4 Combine like terms: 4 + -4 = 0 0 + y = -4.098780306 + -4 y = -4.098780306 + -4 Combine like terms: -4.098780306 + -4 = -8.098780306 y = -8.098780306 Simplifying y = -8.098780306

Solution

The solution to the problem is based on the solutions from the subproblems. y = {0.098780306, -8.098780306}

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