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Simplifying -2(2t2 + -5t + -24) = 0 Reorder the terms: -2(-24 + -5t + 2t2) = 0 (-24 * -2 + -5t * -2 + 2t2 * -2) = 0 (48 + 10t + -4t2) = 0 Solving 48 + 10t + -4t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '2'. 2(24 + 5t + -2t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(24 + 5t + -2t2)' equal to zero and attempt to solve: Simplifying 24 + 5t + -2t2 = 0 Solving 24 + 5t + -2t2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -12 + -2.5t + t2 = 0 Move the constant term to the right: Add '12' to each side of the equation. -12 + -2.5t + 12 + t2 = 0 + 12 Reorder the terms: -12 + 12 + -2.5t + t2 = 0 + 12 Combine like terms: -12 + 12 = 0 0 + -2.5t + t2 = 0 + 12 -2.5t + t2 = 0 + 12 Combine like terms: 0 + 12 = 12 -2.5t + t2 = 12 The t term is -2.5t. Take half its coefficient (-1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. -2.5t + 1.5625 + t2 = 12 + 1.5625 Reorder the terms: 1.5625 + -2.5t + t2 = 12 + 1.5625 Combine like terms: 12 + 1.5625 = 13.5625 1.5625 + -2.5t + t2 = 13.5625 Factor a perfect square on the left side: (t + -1.25)(t + -1.25) = 13.5625 Calculate the square root of the right side: 3.682729966 Break this problem into two subproblems by setting (t + -1.25) equal to 3.682729966 and -3.682729966.Subproblem 1
t + -1.25 = 3.682729966 Simplifying t + -1.25 = 3.682729966 Reorder the terms: -1.25 + t = 3.682729966 Solving -1.25 + t = 3.682729966 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + t = 3.682729966 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + t = 3.682729966 + 1.25 t = 3.682729966 + 1.25 Combine like terms: 3.682729966 + 1.25 = 4.932729966 t = 4.932729966 Simplifying t = 4.932729966Subproblem 2
t + -1.25 = -3.682729966 Simplifying t + -1.25 = -3.682729966 Reorder the terms: -1.25 + t = -3.682729966 Solving -1.25 + t = -3.682729966 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + t = -3.682729966 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + t = -3.682729966 + 1.25 t = -3.682729966 + 1.25 Combine like terms: -3.682729966 + 1.25 = -2.432729966 t = -2.432729966 Simplifying t = -2.432729966Solution
The solution to the problem is based on the solutions from the subproblems. t = {4.932729966, -2.432729966}Solution
t = {4.932729966, -2.432729966}
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