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Simplifying 2y2 + -30y + 66 = 0 Reorder the terms: 66 + -30y + 2y2 = 0 Solving 66 + -30y + 2y2 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), '2'. 2(33 + -15y + y2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(33 + -15y + y2)' equal to zero and attempt to solve: Simplifying 33 + -15y + y2 = 0 Solving 33 + -15y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '-33' to each side of the equation. 33 + -15y + -33 + y2 = 0 + -33 Reorder the terms: 33 + -33 + -15y + y2 = 0 + -33 Combine like terms: 33 + -33 = 0 0 + -15y + y2 = 0 + -33 -15y + y2 = 0 + -33 Combine like terms: 0 + -33 = -33 -15y + y2 = -33 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 = -33 + 56.25 Reorder the terms: 56.25 + -15y + y2 = -33 + 56.25 Combine like terms: -33 + 56.25 = 23.25 56.25 + -15y + y2 = 23.25 Factor a perfect square on the left side: (y + -7.5)(y + -7.5) = 23.25 Calculate the square root of the right side: 4.82182538 Break this problem into two subproblems by setting (y + -7.5) equal to 4.82182538 and -4.82182538.Subproblem 1
y + -7.5 = 4.82182538 Simplifying y + -7.5 = 4.82182538 Reorder the terms: -7.5 + y = 4.82182538 Solving -7.5 + y = 4.82182538 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 = 4.82182538 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + y = 4.82182538 + 7.5 y = 4.82182538 + 7.5 Combine like terms: 4.82182538 + 7.5 = 12.32182538 y = 12.32182538 Simplifying y = 12.32182538Subproblem 2
y + -7.5 = -4.82182538 Simplifying y + -7.5 = -4.82182538 Reorder the terms: -7.5 + y = -4.82182538 Solving -7.5 + y = -4.82182538 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 = -4.82182538 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + y = -4.82182538 + 7.5 y = -4.82182538 + 7.5 Combine like terms: -4.82182538 + 7.5 = 2.67817462 y = 2.67817462 Simplifying y = 2.67817462Solution
The solution to the problem is based on the solutions from the subproblems. y = {12.32182538, 2.67817462}Solution
y = {12.32182538, 2.67817462}
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