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Simplifying 100(t) = -16t2 + 100 Reorder the terms: 100t = 100 + -16t2 Solving 100t = 100 + -16t2 Solving for variable 't'. Reorder the terms: -100 + 100t + 16t2 = 100 + -16t2 + -100 + 16t2 Reorder the terms: -100 + 100t + 16t2 = 100 + -100 + -16t2 + 16t2 Combine like terms: 100 + -100 = 0 -100 + 100t + 16t2 = 0 + -16t2 + 16t2 -100 + 100t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -100 + 100t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-25 + 25t + 4t2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-25 + 25t + 4t2)' equal to zero and attempt to solve: Simplifying -25 + 25t + 4t2 = 0 Solving -25 + 25t + 4t2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -6.25 + 6.25t + t2 = 0 Move the constant term to the right: Add '6.25' to each side of the equation. -6.25 + 6.25t + 6.25 + t2 = 0 + 6.25 Reorder the terms: -6.25 + 6.25 + 6.25t + t2 = 0 + 6.25 Combine like terms: -6.25 + 6.25 = 0.00 0.00 + 6.25t + t2 = 0 + 6.25 6.25t + t2 = 0 + 6.25 Combine like terms: 0 + 6.25 = 6.25 6.25t + t2 = 6.25 The t term is 6.25t. Take half its coefficient (3.125). Square it (9.765625) and add it to both sides. Add '9.765625' to each side of the equation. 6.25t + 9.765625 + t2 = 6.25 + 9.765625 Reorder the terms: 9.765625 + 6.25t + t2 = 6.25 + 9.765625 Combine like terms: 6.25 + 9.765625 = 16.015625 9.765625 + 6.25t + t2 = 16.015625 Factor a perfect square on the left side: (t + 3.125)(t + 3.125) = 16.015625 Calculate the square root of the right side: 4.001952648 Break this problem into two subproblems by setting (t + 3.125) equal to 4.001952648 and -4.001952648.Subproblem 1
t + 3.125 = 4.001952648 Simplifying t + 3.125 = 4.001952648 Reorder the terms: 3.125 + t = 4.001952648 Solving 3.125 + t = 4.001952648 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-3.125' to each side of the equation. 3.125 + -3.125 + t = 4.001952648 + -3.125 Combine like terms: 3.125 + -3.125 = 0.000 0.000 + t = 4.001952648 + -3.125 t = 4.001952648 + -3.125 Combine like terms: 4.001952648 + -3.125 = 0.876952648 t = 0.876952648 Simplifying t = 0.876952648Subproblem 2
t + 3.125 = -4.001952648 Simplifying t + 3.125 = -4.001952648 Reorder the terms: 3.125 + t = -4.001952648 Solving 3.125 + t = -4.001952648 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-3.125' to each side of the equation. 3.125 + -3.125 + t = -4.001952648 + -3.125 Combine like terms: 3.125 + -3.125 = 0.000 0.000 + t = -4.001952648 + -3.125 t = -4.001952648 + -3.125 Combine like terms: -4.001952648 + -3.125 = -7.126952648 t = -7.126952648 Simplifying t = -7.126952648Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.876952648, -7.126952648}Solution
t = {0.876952648, -7.126952648}
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