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Simplifying 0 = -8y2 + 950y + -2250 Reorder the terms: 0 = -2250 + 950y + -8y2 Solving 0 = -2250 + 950y + -8y2 Solving for variable 'y'. Combine like terms: 0 + 2250 = 2250 2250 + -950y + 8y2 = -2250 + 950y + -8y2 + 2250 + -950y + 8y2 Reorder the terms: 2250 + -950y + 8y2 = -2250 + 2250 + 950y + -950y + -8y2 + 8y2 Combine like terms: -2250 + 2250 = 0 2250 + -950y + 8y2 = 0 + 950y + -950y + -8y2 + 8y2 2250 + -950y + 8y2 = 950y + -950y + -8y2 + 8y2 Combine like terms: 950y + -950y = 0 2250 + -950y + 8y2 = 0 + -8y2 + 8y2 2250 + -950y + 8y2 = -8y2 + 8y2 Combine like terms: -8y2 + 8y2 = 0 2250 + -950y + 8y2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(1125 + -475y + 4y2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(1125 + -475y + 4y2)' equal to zero and attempt to solve: Simplifying 1125 + -475y + 4y2 = 0 Solving 1125 + -475y + 4y2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 281.25 + -118.75y + y2 = 0 Move the constant term to the right: Add '-281.25' to each side of the equation. 281.25 + -118.75y + -281.25 + y2 = 0 + -281.25 Reorder the terms: 281.25 + -281.25 + -118.75y + y2 = 0 + -281.25 Combine like terms: 281.25 + -281.25 = 0.00 0.00 + -118.75y + y2 = 0 + -281.25 -118.75y + y2 = 0 + -281.25 Combine like terms: 0 + -281.25 = -281.25 -118.75y + y2 = -281.25 The y term is -118.75y. Take half its coefficient (-59.375). Square it (3525.390625) and add it to both sides. Add '3525.390625' to each side of the equation. -118.75y + 3525.390625 + y2 = -281.25 + 3525.390625 Reorder the terms: 3525.390625 + -118.75y + y2 = -281.25 + 3525.390625 Combine like terms: -281.25 + 3525.390625 = 3244.140625 3525.390625 + -118.75y + y2 = 3244.140625 Factor a perfect square on the left side: (y + -59.375)(y + -59.375) = 3244.140625 Calculate the square root of the right side: 56.957357953 Break this problem into two subproblems by setting (y + -59.375) equal to 56.957357953 and -56.957357953.Subproblem 1
y + -59.375 = 56.957357953 Simplifying y + -59.375 = 56.957357953 Reorder the terms: -59.375 + y = 56.957357953 Solving -59.375 + y = 56.957357953 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '59.375' to each side of the equation. -59.375 + 59.375 + y = 56.957357953 + 59.375 Combine like terms: -59.375 + 59.375 = 0.000 0.000 + y = 56.957357953 + 59.375 y = 56.957357953 + 59.375 Combine like terms: 56.957357953 + 59.375 = 116.332357953 y = 116.332357953 Simplifying y = 116.332357953Subproblem 2
y + -59.375 = -56.957357953 Simplifying y + -59.375 = -56.957357953 Reorder the terms: -59.375 + y = -56.957357953 Solving -59.375 + y = -56.957357953 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '59.375' to each side of the equation. -59.375 + 59.375 + y = -56.957357953 + 59.375 Combine like terms: -59.375 + 59.375 = 0.000 0.000 + y = -56.957357953 + 59.375 y = -56.957357953 + 59.375 Combine like terms: -56.957357953 + 59.375 = 2.417642047 y = 2.417642047 Simplifying y = 2.417642047Solution
The solution to the problem is based on the solutions from the subproblems. y = {116.332357953, 2.417642047}Solution
y = {116.332357953, 2.417642047}
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