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Simplifying 20000 = -8y2 + 950y + -2250 Reorder the terms: 20000 = -2250 + 950y + -8y2 Solving 20000 = -2250 + 950y + -8y2 Solving for variable 'y'. Combine like terms: 20000 + 2250 = 22250 22250 + -950y + 8y2 = -2250 + 950y + -8y2 + 2250 + -950y + 8y2 Reorder the terms: 22250 + -950y + 8y2 = -2250 + 2250 + 950y + -950y + -8y2 + 8y2 Combine like terms: -2250 + 2250 = 0 22250 + -950y + 8y2 = 0 + 950y + -950y + -8y2 + 8y2 22250 + -950y + 8y2 = 950y + -950y + -8y2 + 8y2 Combine like terms: 950y + -950y = 0 22250 + -950y + 8y2 = 0 + -8y2 + 8y2 22250 + -950y + 8y2 = -8y2 + 8y2 Combine like terms: -8y2 + 8y2 = 0 22250 + -950y + 8y2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(11125 + -475y + 4y2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(11125 + -475y + 4y2)' equal to zero and attempt to solve: Simplifying 11125 + -475y + 4y2 = 0 Solving 11125 + -475y + 4y2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 2781.25 + -118.75y + y2 = 0 Move the constant term to the right: Add '-2781.25' to each side of the equation. 2781.25 + -118.75y + -2781.25 + y2 = 0 + -2781.25 Reorder the terms: 2781.25 + -2781.25 + -118.75y + y2 = 0 + -2781.25 Combine like terms: 2781.25 + -2781.25 = 0.00 0.00 + -118.75y + y2 = 0 + -2781.25 -118.75y + y2 = 0 + -2781.25 Combine like terms: 0 + -2781.25 = -2781.25 -118.75y + y2 = -2781.25 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 = -2781.25 + 3525.390625 Reorder the terms: 3525.390625 + -118.75y + y2 = -2781.25 + 3525.390625 Combine like terms: -2781.25 + 3525.390625 = 744.140625 3525.390625 + -118.75y + y2 = 744.140625 Factor a perfect square on the left side: (y + -59.375)(y + -59.375) = 744.140625 Calculate the square root of the right side: 27.278941053 Break this problem into two subproblems by setting (y + -59.375) equal to 27.278941053 and -27.278941053.Subproblem 1
y + -59.375 = 27.278941053 Simplifying y + -59.375 = 27.278941053 Reorder the terms: -59.375 + y = 27.278941053 Solving -59.375 + y = 27.278941053 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 = 27.278941053 + 59.375 Combine like terms: -59.375 + 59.375 = 0.000 0.000 + y = 27.278941053 + 59.375 y = 27.278941053 + 59.375 Combine like terms: 27.278941053 + 59.375 = 86.653941053 y = 86.653941053 Simplifying y = 86.653941053Subproblem 2
y + -59.375 = -27.278941053 Simplifying y + -59.375 = -27.278941053 Reorder the terms: -59.375 + y = -27.278941053 Solving -59.375 + y = -27.278941053 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 = -27.278941053 + 59.375 Combine like terms: -59.375 + 59.375 = 0.000 0.000 + y = -27.278941053 + 59.375 y = -27.278941053 + 59.375 Combine like terms: -27.278941053 + 59.375 = 32.096058947 y = 32.096058947 Simplifying y = 32.096058947Solution
The solution to the problem is based on the solutions from the subproblems. y = {86.653941053, 32.096058947}Solution
y = {86.653941053, 32.096058947}
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