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Simplifying 16t2 + -300t + 500 = 0 Reorder the terms: 500 + -300t + 16t2 = 0 Solving 500 + -300t + 16t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '4'. 4(125 + -75t + 4t2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(125 + -75t + 4t2)' equal to zero and attempt to solve: Simplifying 125 + -75t + 4t2 = 0 Solving 125 + -75t + 4t2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 31.25 + -18.75t + t2 = 0 Move the constant term to the right: Add '-31.25' to each side of the equation. 31.25 + -18.75t + -31.25 + t2 = 0 + -31.25 Reorder the terms: 31.25 + -31.25 + -18.75t + t2 = 0 + -31.25 Combine like terms: 31.25 + -31.25 = 0.00 0.00 + -18.75t + t2 = 0 + -31.25 -18.75t + t2 = 0 + -31.25 Combine like terms: 0 + -31.25 = -31.25 -18.75t + t2 = -31.25 The t term is -18.75t. Take half its coefficient (-9.375). Square it (87.890625) and add it to both sides. Add '87.890625' to each side of the equation. -18.75t + 87.890625 + t2 = -31.25 + 87.890625 Reorder the terms: 87.890625 + -18.75t + t2 = -31.25 + 87.890625 Combine like terms: -31.25 + 87.890625 = 56.640625 87.890625 + -18.75t + t2 = 56.640625 Factor a perfect square on the left side: (t + -9.375)(t + -9.375) = 56.640625 Calculate the square root of the right side: 7.525996612 Break this problem into two subproblems by setting (t + -9.375) equal to 7.525996612 and -7.525996612.Subproblem 1
t + -9.375 = 7.525996612 Simplifying t + -9.375 = 7.525996612 Reorder the terms: -9.375 + t = 7.525996612 Solving -9.375 + t = 7.525996612 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '9.375' to each side of the equation. -9.375 + 9.375 + t = 7.525996612 + 9.375 Combine like terms: -9.375 + 9.375 = 0.000 0.000 + t = 7.525996612 + 9.375 t = 7.525996612 + 9.375 Combine like terms: 7.525996612 + 9.375 = 16.900996612 t = 16.900996612 Simplifying t = 16.900996612Subproblem 2
t + -9.375 = -7.525996612 Simplifying t + -9.375 = -7.525996612 Reorder the terms: -9.375 + t = -7.525996612 Solving -9.375 + t = -7.525996612 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '9.375' to each side of the equation. -9.375 + 9.375 + t = -7.525996612 + 9.375 Combine like terms: -9.375 + 9.375 = 0.000 0.000 + t = -7.525996612 + 9.375 t = -7.525996612 + 9.375 Combine like terms: -7.525996612 + 9.375 = 1.849003388 t = 1.849003388 Simplifying t = 1.849003388Solution
The solution to the problem is based on the solutions from the subproblems. t = {16.900996612, 1.849003388}Solution
t = {16.900996612, 1.849003388}
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