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Simplifying 0 = -16t2 + 36t + -10 Reorder the terms: 0 = -10 + 36t + -16t2 Solving 0 = -10 + 36t + -16t2 Solving for variable 't'. Combine like terms: 0 + 10 = 10 10 + -36t + 16t2 = -10 + 36t + -16t2 + 10 + -36t + 16t2 Reorder the terms: 10 + -36t + 16t2 = -10 + 10 + 36t + -36t + -16t2 + 16t2 Combine like terms: -10 + 10 = 0 10 + -36t + 16t2 = 0 + 36t + -36t + -16t2 + 16t2 10 + -36t + 16t2 = 36t + -36t + -16t2 + 16t2 Combine like terms: 36t + -36t = 0 10 + -36t + 16t2 = 0 + -16t2 + 16t2 10 + -36t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 10 + -36t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(5 + -18t + 8t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(5 + -18t + 8t2)' equal to zero and attempt to solve: Simplifying 5 + -18t + 8t2 = 0 Solving 5 + -18t + 8t2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 0.625 + -2.25t + t2 = 0 Move the constant term to the right: Add '-0.625' to each side of the equation. 0.625 + -2.25t + -0.625 + t2 = 0 + -0.625 Reorder the terms: 0.625 + -0.625 + -2.25t + t2 = 0 + -0.625 Combine like terms: 0.625 + -0.625 = 0.000 0.000 + -2.25t + t2 = 0 + -0.625 -2.25t + t2 = 0 + -0.625 Combine like terms: 0 + -0.625 = -0.625 -2.25t + t2 = -0.625 The t term is -2.25t. Take half its coefficient (-1.125). Square it (1.265625) and add it to both sides. Add '1.265625' to each side of the equation. -2.25t + 1.265625 + t2 = -0.625 + 1.265625 Reorder the terms: 1.265625 + -2.25t + t2 = -0.625 + 1.265625 Combine like terms: -0.625 + 1.265625 = 0.640625 1.265625 + -2.25t + t2 = 0.640625 Factor a perfect square on the left side: (t + -1.125)(t + -1.125) = 0.640625 Calculate the square root of the right side: 0.80039053 Break this problem into two subproblems by setting (t + -1.125) equal to 0.80039053 and -0.80039053.Subproblem 1
t + -1.125 = 0.80039053 Simplifying t + -1.125 = 0.80039053 Reorder the terms: -1.125 + t = 0.80039053 Solving -1.125 + t = 0.80039053 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.125' to each side of the equation. -1.125 + 1.125 + t = 0.80039053 + 1.125 Combine like terms: -1.125 + 1.125 = 0.000 0.000 + t = 0.80039053 + 1.125 t = 0.80039053 + 1.125 Combine like terms: 0.80039053 + 1.125 = 1.92539053 t = 1.92539053 Simplifying t = 1.92539053Subproblem 2
t + -1.125 = -0.80039053 Simplifying t + -1.125 = -0.80039053 Reorder the terms: -1.125 + t = -0.80039053 Solving -1.125 + t = -0.80039053 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.125' to each side of the equation. -1.125 + 1.125 + t = -0.80039053 + 1.125 Combine like terms: -1.125 + 1.125 = 0.000 0.000 + t = -0.80039053 + 1.125 t = -0.80039053 + 1.125 Combine like terms: -0.80039053 + 1.125 = 0.32460947 t = 0.32460947 Simplifying t = 0.32460947Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.92539053, 0.32460947}Solution
t = {1.92539053, 0.32460947}
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