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Simplifying 6y2 + -102y + 336 = 0 Reorder the terms: 336 + -102y + 6y2 = 0 Solving 336 + -102y + 6y2 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), '6'. 6(56 + -17y + y2) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(56 + -17y + y2)' equal to zero and attempt to solve: Simplifying 56 + -17y + y2 = 0 Solving 56 + -17y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '-56' to each side of the equation. 56 + -17y + -56 + y2 = 0 + -56 Reorder the terms: 56 + -56 + -17y + y2 = 0 + -56 Combine like terms: 56 + -56 = 0 0 + -17y + y2 = 0 + -56 -17y + y2 = 0 + -56 Combine like terms: 0 + -56 = -56 -17y + y2 = -56 The y term is -17y. Take half its coefficient (-8.5). Square it (72.25) and add it to both sides. Add '72.25' to each side of the equation. -17y + 72.25 + y2 = -56 + 72.25 Reorder the terms: 72.25 + -17y + y2 = -56 + 72.25 Combine like terms: -56 + 72.25 = 16.25 72.25 + -17y + y2 = 16.25 Factor a perfect square on the left side: (y + -8.5)(y + -8.5) = 16.25 Calculate the square root of the right side: 4.031128874 Break this problem into two subproblems by setting (y + -8.5) equal to 4.031128874 and -4.031128874.Subproblem 1
y + -8.5 = 4.031128874 Simplifying y + -8.5 = 4.031128874 Reorder the terms: -8.5 + y = 4.031128874 Solving -8.5 + y = 4.031128874 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '8.5' to each side of the equation. -8.5 + 8.5 + y = 4.031128874 + 8.5 Combine like terms: -8.5 + 8.5 = 0.0 0.0 + y = 4.031128874 + 8.5 y = 4.031128874 + 8.5 Combine like terms: 4.031128874 + 8.5 = 12.531128874 y = 12.531128874 Simplifying y = 12.531128874Subproblem 2
y + -8.5 = -4.031128874 Simplifying y + -8.5 = -4.031128874 Reorder the terms: -8.5 + y = -4.031128874 Solving -8.5 + y = -4.031128874 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '8.5' to each side of the equation. -8.5 + 8.5 + y = -4.031128874 + 8.5 Combine like terms: -8.5 + 8.5 = 0.0 0.0 + y = -4.031128874 + 8.5 y = -4.031128874 + 8.5 Combine like terms: -4.031128874 + 8.5 = 4.468871126 y = 4.468871126 Simplifying y = 4.468871126Solution
The solution to the problem is based on the solutions from the subproblems. y = {12.531128874, 4.468871126}Solution
y = {12.531128874, 4.468871126}
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