2y^2-7y-10=0

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Solution for 2y^2-7y-10=0 equation:


Simplifying
2y2 + -7y + -10 = 0

Reorder the terms:
-10 + -7y + 2y2 = 0

Solving
-10 + -7y + 2y2 = 0

Solving for variable 'y'.

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

Divide each side by '2'.
-5 + -3.5y + y2 = 0

Move the constant term to the right:

Add '5' to each side of the equation.
-5 + -3.5y + 5 + y2 = 0 + 5

Reorder the terms:
-5 + 5 + -3.5y + y2 = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -3.5y + y2 = 0 + 5
-3.5y + y2 = 0 + 5

Combine like terms: 0 + 5 = 5
-3.5y + y2 = 5

The y term is -3.5y.  Take half its coefficient (-1.75).
Square it (3.0625) and add it to both sides.

Add '3.0625' to each side of the equation.
-3.5y + 3.0625 + y2 = 5 + 3.0625

Reorder the terms:
3.0625 + -3.5y + y2 = 5 + 3.0625

Combine like terms: 5 + 3.0625 = 8.0625
3.0625 + -3.5y + y2 = 8.0625

Factor a perfect square on the left side:
(y + -1.75)(y + -1.75) = 8.0625

Calculate the square root of the right side: 2.839454173

Break this problem into two subproblems by setting 
(y + -1.75) equal to 2.839454173 and -2.839454173.

Subproblem 1

y + -1.75 = 2.839454173 Simplifying y + -1.75 = 2.839454173 Reorder the terms: -1.75 + y = 2.839454173 Solving -1.75 + y = 2.839454173 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1.75' to each side of the equation. -1.75 + 1.75 + y = 2.839454173 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + y = 2.839454173 + 1.75 y = 2.839454173 + 1.75 Combine like terms: 2.839454173 + 1.75 = 4.589454173 y = 4.589454173 Simplifying y = 4.589454173

Subproblem 2

y + -1.75 = -2.839454173 Simplifying y + -1.75 = -2.839454173 Reorder the terms: -1.75 + y = -2.839454173 Solving -1.75 + y = -2.839454173 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1.75' to each side of the equation. -1.75 + 1.75 + y = -2.839454173 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + y = -2.839454173 + 1.75 y = -2.839454173 + 1.75 Combine like terms: -2.839454173 + 1.75 = -1.089454173 y = -1.089454173 Simplifying y = -1.089454173

Solution

The solution to the problem is based on the solutions from the subproblems. y = {4.589454173, -1.089454173}

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