2y^2+68y-48=0

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Solution for 2y^2+68y-48=0 equation:


Simplifying
2y2 + 68y + -48 = 0

Reorder the terms:
-48 + 68y + 2y2 = 0

Solving
-48 + 68y + 2y2 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-24 + 34y + y2) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(-24 + 34y + y2)' equal to zero and attempt to solve: Simplifying -24 + 34y + y2 = 0 Solving -24 + 34y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '24' to each side of the equation. -24 + 34y + 24 + y2 = 0 + 24 Reorder the terms: -24 + 24 + 34y + y2 = 0 + 24 Combine like terms: -24 + 24 = 0 0 + 34y + y2 = 0 + 24 34y + y2 = 0 + 24 Combine like terms: 0 + 24 = 24 34y + y2 = 24 The y term is 34y. Take half its coefficient (17). Square it (289) and add it to both sides. Add '289' to each side of the equation. 34y + 289 + y2 = 24 + 289 Reorder the terms: 289 + 34y + y2 = 24 + 289 Combine like terms: 24 + 289 = 313 289 + 34y + y2 = 313 Factor a perfect square on the left side: (y + 17)(y + 17) = 313 Calculate the square root of the right side: 17.691806013 Break this problem into two subproblems by setting (y + 17) equal to 17.691806013 and -17.691806013.

Subproblem 1

y + 17 = 17.691806013 Simplifying y + 17 = 17.691806013 Reorder the terms: 17 + y = 17.691806013 Solving 17 + y = 17.691806013 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-17' to each side of the equation. 17 + -17 + y = 17.691806013 + -17 Combine like terms: 17 + -17 = 0 0 + y = 17.691806013 + -17 y = 17.691806013 + -17 Combine like terms: 17.691806013 + -17 = 0.691806013 y = 0.691806013 Simplifying y = 0.691806013

Subproblem 2

y + 17 = -17.691806013 Simplifying y + 17 = -17.691806013 Reorder the terms: 17 + y = -17.691806013 Solving 17 + y = -17.691806013 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-17' to each side of the equation. 17 + -17 + y = -17.691806013 + -17 Combine like terms: 17 + -17 = 0 0 + y = -17.691806013 + -17 y = -17.691806013 + -17 Combine like terms: -17.691806013 + -17 = -34.691806013 y = -34.691806013 Simplifying y = -34.691806013

Solution

The solution to the problem is based on the solutions from the subproblems. y = {0.691806013, -34.691806013}

Solution

y = {0.691806013, -34.691806013}

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