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Simplifying 88 = 240t + -16t2 Solving 88 = 240t + -16t2 Solving for variable 't'. Reorder the terms: 88 + -240t + 16t2 = 240t + -240t + -16t2 + 16t2 Combine like terms: 240t + -240t = 0 88 + -240t + 16t2 = 0 + -16t2 + 16t2 88 + -240t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 88 + -240t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '8'. 8(11 + -30t + 2t2) = 0 Ignore the factor 8.Subproblem 1
Set the factor '(11 + -30t + 2t2)' equal to zero and attempt to solve: Simplifying 11 + -30t + 2t2 = 0 Solving 11 + -30t + 2t2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 5.5 + -15t + t2 = 0 Move the constant term to the right: Add '-5.5' to each side of the equation. 5.5 + -15t + -5.5 + t2 = 0 + -5.5 Reorder the terms: 5.5 + -5.5 + -15t + t2 = 0 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + -15t + t2 = 0 + -5.5 -15t + t2 = 0 + -5.5 Combine like terms: 0 + -5.5 = -5.5 -15t + t2 = -5.5 The t term is -15t. Take half its coefficient (-7.5). Square it (56.25) and add it to both sides. Add '56.25' to each side of the equation. -15t + 56.25 + t2 = -5.5 + 56.25 Reorder the terms: 56.25 + -15t + t2 = -5.5 + 56.25 Combine like terms: -5.5 + 56.25 = 50.75 56.25 + -15t + t2 = 50.75 Factor a perfect square on the left side: (t + -7.5)(t + -7.5) = 50.75 Calculate the square root of the right side: 7.123903424 Break this problem into two subproblems by setting (t + -7.5) equal to 7.123903424 and -7.123903424.Subproblem 1
t + -7.5 = 7.123903424 Simplifying t + -7.5 = 7.123903424 Reorder the terms: -7.5 + t = 7.123903424 Solving -7.5 + t = 7.123903424 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + t = 7.123903424 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + t = 7.123903424 + 7.5 t = 7.123903424 + 7.5 Combine like terms: 7.123903424 + 7.5 = 14.623903424 t = 14.623903424 Simplifying t = 14.623903424Subproblem 2
t + -7.5 = -7.123903424 Simplifying t + -7.5 = -7.123903424 Reorder the terms: -7.5 + t = -7.123903424 Solving -7.5 + t = -7.123903424 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + t = -7.123903424 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + t = -7.123903424 + 7.5 t = -7.123903424 + 7.5 Combine like terms: -7.123903424 + 7.5 = 0.376096576 t = 0.376096576 Simplifying t = 0.376096576Solution
The solution to the problem is based on the solutions from the subproblems. t = {14.623903424, 0.376096576}Solution
t = {14.623903424, 0.376096576}
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