2y^2-30y+48=0

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Solution for 2y^2-30y+48=0 equation:


Simplifying
2y2 + -30y + 48 = 0

Reorder the terms:
48 + -30y + 2y2 = 0

Solving
48 + -30y + 2y2 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '2'.
2(24 + -15y + y2) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(24 + -15y + y2)' equal to zero and attempt to solve: Simplifying 24 + -15y + y2 = 0 Solving 24 + -15y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '-24' to each side of the equation. 24 + -15y + -24 + y2 = 0 + -24 Reorder the terms: 24 + -24 + -15y + y2 = 0 + -24 Combine like terms: 24 + -24 = 0 0 + -15y + y2 = 0 + -24 -15y + y2 = 0 + -24 Combine like terms: 0 + -24 = -24 -15y + y2 = -24 The y term is -15y. Take half its coefficient (-7.5). Square it (56.25) and add it to both sides. Add '56.25' to each side of the equation. -15y + 56.25 + y2 = -24 + 56.25 Reorder the terms: 56.25 + -15y + y2 = -24 + 56.25 Combine like terms: -24 + 56.25 = 32.25 56.25 + -15y + y2 = 32.25 Factor a perfect square on the left side: (y + -7.5)(y + -7.5) = 32.25 Calculate the square root of the right side: 5.678908346 Break this problem into two subproblems by setting (y + -7.5) equal to 5.678908346 and -5.678908346.

Subproblem 1

y + -7.5 = 5.678908346 Simplifying y + -7.5 = 5.678908346 Reorder the terms: -7.5 + y = 5.678908346 Solving -7.5 + y = 5.678908346 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + y = 5.678908346 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + y = 5.678908346 + 7.5 y = 5.678908346 + 7.5 Combine like terms: 5.678908346 + 7.5 = 13.178908346 y = 13.178908346 Simplifying y = 13.178908346

Subproblem 2

y + -7.5 = -5.678908346 Simplifying y + -7.5 = -5.678908346 Reorder the terms: -7.5 + y = -5.678908346 Solving -7.5 + y = -5.678908346 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + y = -5.678908346 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + y = -5.678908346 + 7.5 y = -5.678908346 + 7.5 Combine like terms: -5.678908346 + 7.5 = 1.821091654 y = 1.821091654 Simplifying y = 1.821091654

Solution

The solution to the problem is based on the solutions from the subproblems. y = {13.178908346, 1.821091654}

Solution

y = {13.178908346, 1.821091654}

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