2y^2-9y-70=0

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Solution for 2y^2-9y-70=0 equation:


Simplifying
2y2 + -9y + -70 = 0

Reorder the terms:
-70 + -9y + 2y2 = 0

Solving
-70 + -9y + 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'.
-35 + -4.5y + y2 = 0

Move the constant term to the right:

Add '35' to each side of the equation.
-35 + -4.5y + 35 + y2 = 0 + 35

Reorder the terms:
-35 + 35 + -4.5y + y2 = 0 + 35

Combine like terms: -35 + 35 = 0
0 + -4.5y + y2 = 0 + 35
-4.5y + y2 = 0 + 35

Combine like terms: 0 + 35 = 35
-4.5y + y2 = 35

The y term is -4.5y.  Take half its coefficient (-2.25).
Square it (5.0625) and add it to both sides.

Add '5.0625' to each side of the equation.
-4.5y + 5.0625 + y2 = 35 + 5.0625

Reorder the terms:
5.0625 + -4.5y + y2 = 35 + 5.0625

Combine like terms: 35 + 5.0625 = 40.0625
5.0625 + -4.5y + y2 = 40.0625

Factor a perfect square on the left side:
(y + -2.25)(y + -2.25) = 40.0625

Calculate the square root of the right side: 6.329494451

Break this problem into two subproblems by setting 
(y + -2.25) equal to 6.329494451 and -6.329494451.

Subproblem 1

y + -2.25 = 6.329494451 Simplifying y + -2.25 = 6.329494451 Reorder the terms: -2.25 + y = 6.329494451 Solving -2.25 + y = 6.329494451 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '2.25' to each side of the equation. -2.25 + 2.25 + y = 6.329494451 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + y = 6.329494451 + 2.25 y = 6.329494451 + 2.25 Combine like terms: 6.329494451 + 2.25 = 8.579494451 y = 8.579494451 Simplifying y = 8.579494451

Subproblem 2

y + -2.25 = -6.329494451 Simplifying y + -2.25 = -6.329494451 Reorder the terms: -2.25 + y = -6.329494451 Solving -2.25 + y = -6.329494451 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '2.25' to each side of the equation. -2.25 + 2.25 + y = -6.329494451 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + y = -6.329494451 + 2.25 y = -6.329494451 + 2.25 Combine like terms: -6.329494451 + 2.25 = -4.079494451 y = -4.079494451 Simplifying y = -4.079494451

Solution

The solution to the problem is based on the solutions from the subproblems. y = {8.579494451, -4.079494451}

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