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Simplifying 8y2 + -10y + -280 = 0 Reorder the terms: -280 + -10y + 8y2 = 0 Solving -280 + -10y + 8y2 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), '2'. 2(-140 + -5y + 4y2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-140 + -5y + 4y2)' equal to zero and attempt to solve: Simplifying -140 + -5y + 4y2 = 0 Solving -140 + -5y + 4y2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -35 + -1.25y + y2 = 0 Move the constant term to the right: Add '35' to each side of the equation. -35 + -1.25y + 35 + y2 = 0 + 35 Reorder the terms: -35 + 35 + -1.25y + y2 = 0 + 35 Combine like terms: -35 + 35 = 0 0 + -1.25y + y2 = 0 + 35 -1.25y + y2 = 0 + 35 Combine like terms: 0 + 35 = 35 -1.25y + y2 = 35 The y term is -1.25y. Take half its coefficient (-0.625). Square it (0.390625) and add it to both sides. Add '0.390625' to each side of the equation. -1.25y + 0.390625 + y2 = 35 + 0.390625 Reorder the terms: 0.390625 + -1.25y + y2 = 35 + 0.390625 Combine like terms: 35 + 0.390625 = 35.390625 0.390625 + -1.25y + y2 = 35.390625 Factor a perfect square on the left side: (y + -0.625)(y + -0.625) = 35.390625 Calculate the square root of the right side: 5.949002017 Break this problem into two subproblems by setting (y + -0.625) equal to 5.949002017 and -5.949002017.Subproblem 1
y + -0.625 = 5.949002017 Simplifying y + -0.625 = 5.949002017 Reorder the terms: -0.625 + y = 5.949002017 Solving -0.625 + y = 5.949002017 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.625' to each side of the equation. -0.625 + 0.625 + y = 5.949002017 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + y = 5.949002017 + 0.625 y = 5.949002017 + 0.625 Combine like terms: 5.949002017 + 0.625 = 6.574002017 y = 6.574002017 Simplifying y = 6.574002017Subproblem 2
y + -0.625 = -5.949002017 Simplifying y + -0.625 = -5.949002017 Reorder the terms: -0.625 + y = -5.949002017 Solving -0.625 + y = -5.949002017 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.625' to each side of the equation. -0.625 + 0.625 + y = -5.949002017 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + y = -5.949002017 + 0.625 y = -5.949002017 + 0.625 Combine like terms: -5.949002017 + 0.625 = -5.324002017 y = -5.324002017 Simplifying y = -5.324002017Solution
The solution to the problem is based on the solutions from the subproblems. y = {6.574002017, -5.324002017}Solution
y = {6.574002017, -5.324002017}
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