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Simplifying -16t2 + -2t + 500 = 0 Reorder the terms: 500 + -2t + -16t2 = 0 Solving 500 + -2t + -16t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '2'. 2(250 + -1t + -8t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(250 + -1t + -8t2)' equal to zero and attempt to solve: Simplifying 250 + -1t + -8t2 = 0 Solving 250 + -1t + -8t2 = 0 Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. -31.25 + 0.125t + t2 = 0 Move the constant term to the right: Add '31.25' to each side of the equation. -31.25 + 0.125t + 31.25 + t2 = 0 + 31.25 Reorder the terms: -31.25 + 31.25 + 0.125t + t2 = 0 + 31.25 Combine like terms: -31.25 + 31.25 = 0.00 0.00 + 0.125t + t2 = 0 + 31.25 0.125t + t2 = 0 + 31.25 Combine like terms: 0 + 31.25 = 31.25 0.125t + t2 = 31.25 The t term is 0.125t. Take half its coefficient (0.0625). Square it (0.00390625) and add it to both sides. Add '0.00390625' to each side of the equation. 0.125t + 0.00390625 + t2 = 31.25 + 0.00390625 Reorder the terms: 0.00390625 + 0.125t + t2 = 31.25 + 0.00390625 Combine like terms: 31.25 + 0.00390625 = 31.25390625 0.00390625 + 0.125t + t2 = 31.25390625 Factor a perfect square on the left side: (t + 0.0625)(t + 0.0625) = 31.25390625 Calculate the square root of the right side: 5.590519318 Break this problem into two subproblems by setting (t + 0.0625) equal to 5.590519318 and -5.590519318.Subproblem 1
t + 0.0625 = 5.590519318 Simplifying t + 0.0625 = 5.590519318 Reorder the terms: 0.0625 + t = 5.590519318 Solving 0.0625 + t = 5.590519318 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.0625' to each side of the equation. 0.0625 + -0.0625 + t = 5.590519318 + -0.0625 Combine like terms: 0.0625 + -0.0625 = 0.0000 0.0000 + t = 5.590519318 + -0.0625 t = 5.590519318 + -0.0625 Combine like terms: 5.590519318 + -0.0625 = 5.528019318 t = 5.528019318 Simplifying t = 5.528019318Subproblem 2
t + 0.0625 = -5.590519318 Simplifying t + 0.0625 = -5.590519318 Reorder the terms: 0.0625 + t = -5.590519318 Solving 0.0625 + t = -5.590519318 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.0625' to each side of the equation. 0.0625 + -0.0625 + t = -5.590519318 + -0.0625 Combine like terms: 0.0625 + -0.0625 = 0.0000 0.0000 + t = -5.590519318 + -0.0625 t = -5.590519318 + -0.0625 Combine like terms: -5.590519318 + -0.0625 = -5.653019318 t = -5.653019318 Simplifying t = -5.653019318Solution
The solution to the problem is based on the solutions from the subproblems. t = {5.528019318, -5.653019318}Solution
t = {5.528019318, -5.653019318}
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