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Simplifying -2t2 + 20t + 24 = 0 Reorder the terms: 24 + 20t + -2t2 = 0 Solving 24 + 20t + -2t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '2'. 2(12 + 10t + -1t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(12 + 10t + -1t2)' equal to zero and attempt to solve: Simplifying 12 + 10t + -1t2 = 0 Solving 12 + 10t + -1t2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -12 + -10t + t2 = 0 Move the constant term to the right: Add '12' to each side of the equation. -12 + -10t + 12 + t2 = 0 + 12 Reorder the terms: -12 + 12 + -10t + t2 = 0 + 12 Combine like terms: -12 + 12 = 0 0 + -10t + t2 = 0 + 12 -10t + t2 = 0 + 12 Combine like terms: 0 + 12 = 12 -10t + t2 = 12 The t term is -10t. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10t + 25 + t2 = 12 + 25 Reorder the terms: 25 + -10t + t2 = 12 + 25 Combine like terms: 12 + 25 = 37 25 + -10t + t2 = 37 Factor a perfect square on the left side: (t + -5)(t + -5) = 37 Calculate the square root of the right side: 6.08276253 Break this problem into two subproblems by setting (t + -5) equal to 6.08276253 and -6.08276253.Subproblem 1
t + -5 = 6.08276253 Simplifying t + -5 = 6.08276253 Reorder the terms: -5 + t = 6.08276253 Solving -5 + t = 6.08276253 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + t = 6.08276253 + 5 Combine like terms: -5 + 5 = 0 0 + t = 6.08276253 + 5 t = 6.08276253 + 5 Combine like terms: 6.08276253 + 5 = 11.08276253 t = 11.08276253 Simplifying t = 11.08276253Subproblem 2
t + -5 = -6.08276253 Simplifying t + -5 = -6.08276253 Reorder the terms: -5 + t = -6.08276253 Solving -5 + t = -6.08276253 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + t = -6.08276253 + 5 Combine like terms: -5 + 5 = 0 0 + t = -6.08276253 + 5 t = -6.08276253 + 5 Combine like terms: -6.08276253 + 5 = -1.08276253 t = -1.08276253 Simplifying t = -1.08276253Solution
The solution to the problem is based on the solutions from the subproblems. t = {11.08276253, -1.08276253}Solution
t = {11.08276253, -1.08276253}
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