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Simplifying -16t2 + 24t + 1200 = 0 Reorder the terms: 1200 + 24t + -16t2 = 0 Solving 1200 + 24t + -16t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '8'. 8(150 + 3t + -2t2) = 0 Ignore the factor 8.Subproblem 1
Set the factor '(150 + 3t + -2t2)' equal to zero and attempt to solve: Simplifying 150 + 3t + -2t2 = 0 Solving 150 + 3t + -2t2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -75 + -1.5t + t2 = 0 Move the constant term to the right: Add '75' to each side of the equation. -75 + -1.5t + 75 + t2 = 0 + 75 Reorder the terms: -75 + 75 + -1.5t + t2 = 0 + 75 Combine like terms: -75 + 75 = 0 0 + -1.5t + t2 = 0 + 75 -1.5t + t2 = 0 + 75 Combine like terms: 0 + 75 = 75 -1.5t + t2 = 75 The t term is -1.5t. Take half its coefficient (-0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. -1.5t + 0.5625 + t2 = 75 + 0.5625 Reorder the terms: 0.5625 + -1.5t + t2 = 75 + 0.5625 Combine like terms: 75 + 0.5625 = 75.5625 0.5625 + -1.5t + t2 = 75.5625 Factor a perfect square on the left side: (t + -0.75)(t + -0.75) = 75.5625 Calculate the square root of the right side: 8.692669325 Break this problem into two subproblems by setting (t + -0.75) equal to 8.692669325 and -8.692669325.Subproblem 1
t + -0.75 = 8.692669325 Simplifying t + -0.75 = 8.692669325 Reorder the terms: -0.75 + t = 8.692669325 Solving -0.75 + t = 8.692669325 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + t = 8.692669325 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + t = 8.692669325 + 0.75 t = 8.692669325 + 0.75 Combine like terms: 8.692669325 + 0.75 = 9.442669325 t = 9.442669325 Simplifying t = 9.442669325Subproblem 2
t + -0.75 = -8.692669325 Simplifying t + -0.75 = -8.692669325 Reorder the terms: -0.75 + t = -8.692669325 Solving -0.75 + t = -8.692669325 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + t = -8.692669325 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + t = -8.692669325 + 0.75 t = -8.692669325 + 0.75 Combine like terms: -8.692669325 + 0.75 = -7.942669325 t = -7.942669325 Simplifying t = -7.942669325Solution
The solution to the problem is based on the solutions from the subproblems. t = {9.442669325, -7.942669325}Solution
t = {9.442669325, -7.942669325}
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