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Simplifying 790(t) = -16t2 + 790 Reorder the terms: 790t = 790 + -16t2 Solving 790t = 790 + -16t2 Solving for variable 't'. Reorder the terms: -790 + 790t + 16t2 = 790 + -16t2 + -790 + 16t2 Reorder the terms: -790 + 790t + 16t2 = 790 + -790 + -16t2 + 16t2 Combine like terms: 790 + -790 = 0 -790 + 790t + 16t2 = 0 + -16t2 + 16t2 -790 + 790t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -790 + 790t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-395 + 395t + 8t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-395 + 395t + 8t2)' equal to zero and attempt to solve: Simplifying -395 + 395t + 8t2 = 0 Solving -395 + 395t + 8t2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -49.375 + 49.375t + t2 = 0 Move the constant term to the right: Add '49.375' to each side of the equation. -49.375 + 49.375t + 49.375 + t2 = 0 + 49.375 Reorder the terms: -49.375 + 49.375 + 49.375t + t2 = 0 + 49.375 Combine like terms: -49.375 + 49.375 = 0.000 0.000 + 49.375t + t2 = 0 + 49.375 49.375t + t2 = 0 + 49.375 Combine like terms: 0 + 49.375 = 49.375 49.375t + t2 = 49.375 The t term is 49.375t. Take half its coefficient (24.6875). Square it (609.4726563) and add it to both sides. Add '609.4726563' to each side of the equation. 49.375t + 609.4726563 + t2 = 49.375 + 609.4726563 Reorder the terms: 609.4726563 + 49.375t + t2 = 49.375 + 609.4726563 Combine like terms: 49.375 + 609.4726563 = 658.8476563 609.4726563 + 49.375t + t2 = 658.8476563 Factor a perfect square on the left side: (t + 24.6875)(t + 24.6875) = 658.8476563 Calculate the square root of the right side: 25.6680279 Break this problem into two subproblems by setting (t + 24.6875) equal to 25.6680279 and -25.6680279.Subproblem 1
t + 24.6875 = 25.6680279 Simplifying t + 24.6875 = 25.6680279 Reorder the terms: 24.6875 + t = 25.6680279 Solving 24.6875 + t = 25.6680279 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-24.6875' to each side of the equation. 24.6875 + -24.6875 + t = 25.6680279 + -24.6875 Combine like terms: 24.6875 + -24.6875 = 0.0000 0.0000 + t = 25.6680279 + -24.6875 t = 25.6680279 + -24.6875 Combine like terms: 25.6680279 + -24.6875 = 0.9805279 t = 0.9805279 Simplifying t = 0.9805279Subproblem 2
t + 24.6875 = -25.6680279 Simplifying t + 24.6875 = -25.6680279 Reorder the terms: 24.6875 + t = -25.6680279 Solving 24.6875 + t = -25.6680279 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-24.6875' to each side of the equation. 24.6875 + -24.6875 + t = -25.6680279 + -24.6875 Combine like terms: 24.6875 + -24.6875 = 0.0000 0.0000 + t = -25.6680279 + -24.6875 t = -25.6680279 + -24.6875 Combine like terms: -25.6680279 + -24.6875 = -50.3555279 t = -50.3555279 Simplifying t = -50.3555279Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.9805279, -50.3555279}Solution
t = {0.9805279, -50.3555279}
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