7y^2+8y+2=0

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Solution for 7y^2+8y+2=0 equation:


Simplifying
7y2 + 8y + 2 = 0

Reorder the terms:
2 + 8y + 7y2 = 0

Solving
2 + 8y + 7y2 = 0

Solving for variable 'y'.

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

Divide each side by '7'.
0.2857142857 + 1.142857143y + y2 = 0

Move the constant term to the right:

Add '-0.2857142857' to each side of the equation.
0.2857142857 + 1.142857143y + -0.2857142857 + y2 = 0 + -0.2857142857

Reorder the terms:
0.2857142857 + -0.2857142857 + 1.142857143y + y2 = 0 + -0.2857142857

Combine like terms: 0.2857142857 + -0.2857142857 = 0.0000000000
0.0000000000 + 1.142857143y + y2 = 0 + -0.2857142857
1.142857143y + y2 = 0 + -0.2857142857

Combine like terms: 0 + -0.2857142857 = -0.2857142857
1.142857143y + y2 = -0.2857142857

The y term is 1.142857143y.  Take half its coefficient (0.5714285715).
Square it (0.3265306123) and add it to both sides.

Add '0.3265306123' to each side of the equation.
1.142857143y + 0.3265306123 + y2 = -0.2857142857 + 0.3265306123

Reorder the terms:
0.3265306123 + 1.142857143y + y2 = -0.2857142857 + 0.3265306123

Combine like terms: -0.2857142857 + 0.3265306123 = 0.0408163266
0.3265306123 + 1.142857143y + y2 = 0.0408163266

Factor a perfect square on the left side:
(y + 0.5714285715)(y + 0.5714285715) = 0.0408163266

Calculate the square root of the right side: 0.202030509

Break this problem into two subproblems by setting 
(y + 0.5714285715) equal to 0.202030509 and -0.202030509.

Subproblem 1

y + 0.5714285715 = 0.202030509 Simplifying y + 0.5714285715 = 0.202030509 Reorder the terms: 0.5714285715 + y = 0.202030509 Solving 0.5714285715 + y = 0.202030509 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.5714285715' to each side of the equation. 0.5714285715 + -0.5714285715 + y = 0.202030509 + -0.5714285715 Combine like terms: 0.5714285715 + -0.5714285715 = 0.0000000000 0.0000000000 + y = 0.202030509 + -0.5714285715 y = 0.202030509 + -0.5714285715 Combine like terms: 0.202030509 + -0.5714285715 = -0.3693980625 y = -0.3693980625 Simplifying y = -0.3693980625

Subproblem 2

y + 0.5714285715 = -0.202030509 Simplifying y + 0.5714285715 = -0.202030509 Reorder the terms: 0.5714285715 + y = -0.202030509 Solving 0.5714285715 + y = -0.202030509 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.5714285715' to each side of the equation. 0.5714285715 + -0.5714285715 + y = -0.202030509 + -0.5714285715 Combine like terms: 0.5714285715 + -0.5714285715 = 0.0000000000 0.0000000000 + y = -0.202030509 + -0.5714285715 y = -0.202030509 + -0.5714285715 Combine like terms: -0.202030509 + -0.5714285715 = -0.7734590805 y = -0.7734590805 Simplifying y = -0.7734590805

Solution

The solution to the problem is based on the solutions from the subproblems. y = {-0.3693980625, -0.7734590805}

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