5y^2+21y=4

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Solution for 5y^2+21y=4 equation:


Simplifying
5y2 + 21y = 4

Reorder the terms:
21y + 5y2 = 4

Solving
21y + 5y2 = 4

Solving for variable 'y'.

Reorder the terms:
-4 + 21y + 5y2 = 4 + -4

Combine like terms: 4 + -4 = 0
-4 + 21y + 5y2 = 0

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

Divide each side by '5'.
-0.8 + 4.2y + y2 = 0

Move the constant term to the right:

Add '0.8' to each side of the equation.
-0.8 + 4.2y + 0.8 + y2 = 0 + 0.8

Reorder the terms:
-0.8 + 0.8 + 4.2y + y2 = 0 + 0.8

Combine like terms: -0.8 + 0.8 = 0.0
0.0 + 4.2y + y2 = 0 + 0.8
4.2y + y2 = 0 + 0.8

Combine like terms: 0 + 0.8 = 0.8
4.2y + y2 = 0.8

The y term is 4.2y.  Take half its coefficient (2.1).
Square it (4.41) and add it to both sides.

Add '4.41' to each side of the equation.
4.2y + 4.41 + y2 = 0.8 + 4.41

Reorder the terms:
4.41 + 4.2y + y2 = 0.8 + 4.41

Combine like terms: 0.8 + 4.41 = 5.21
4.41 + 4.2y + y2 = 5.21

Factor a perfect square on the left side:
(y + 2.1)(y + 2.1) = 5.21

Calculate the square root of the right side: 2.282542442

Break this problem into two subproblems by setting 
(y + 2.1) equal to 2.282542442 and -2.282542442.

Subproblem 1

y + 2.1 = 2.282542442 Simplifying y + 2.1 = 2.282542442 Reorder the terms: 2.1 + y = 2.282542442 Solving 2.1 + y = 2.282542442 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-2.1' to each side of the equation. 2.1 + -2.1 + y = 2.282542442 + -2.1 Combine like terms: 2.1 + -2.1 = 0.0 0.0 + y = 2.282542442 + -2.1 y = 2.282542442 + -2.1 Combine like terms: 2.282542442 + -2.1 = 0.182542442 y = 0.182542442 Simplifying y = 0.182542442

Subproblem 2

y + 2.1 = -2.282542442 Simplifying y + 2.1 = -2.282542442 Reorder the terms: 2.1 + y = -2.282542442 Solving 2.1 + y = -2.282542442 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-2.1' to each side of the equation. 2.1 + -2.1 + y = -2.282542442 + -2.1 Combine like terms: 2.1 + -2.1 = 0.0 0.0 + y = -2.282542442 + -2.1 y = -2.282542442 + -2.1 Combine like terms: -2.282542442 + -2.1 = -4.382542442 y = -4.382542442 Simplifying y = -4.382542442

Solution

The solution to the problem is based on the solutions from the subproblems. y = {0.182542442, -4.382542442}

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