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Simplifying 16t2 + -144t + 280 = 0 Reorder the terms: 280 + -144t + 16t2 = 0 Solving 280 + -144t + 16t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '8'. 8(35 + -18t + 2t2) = 0 Ignore the factor 8.Subproblem 1
Set the factor '(35 + -18t + 2t2)' equal to zero and attempt to solve: Simplifying 35 + -18t + 2t2 = 0 Solving 35 + -18t + 2t2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 17.5 + -9t + t2 = 0 Move the constant term to the right: Add '-17.5' to each side of the equation. 17.5 + -9t + -17.5 + t2 = 0 + -17.5 Reorder the terms: 17.5 + -17.5 + -9t + t2 = 0 + -17.5 Combine like terms: 17.5 + -17.5 = 0.0 0.0 + -9t + t2 = 0 + -17.5 -9t + t2 = 0 + -17.5 Combine like terms: 0 + -17.5 = -17.5 -9t + t2 = -17.5 The t term is -9t. Take half its coefficient (-4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. -9t + 20.25 + t2 = -17.5 + 20.25 Reorder the terms: 20.25 + -9t + t2 = -17.5 + 20.25 Combine like terms: -17.5 + 20.25 = 2.75 20.25 + -9t + t2 = 2.75 Factor a perfect square on the left side: (t + -4.5)(t + -4.5) = 2.75 Calculate the square root of the right side: 1.658312395 Break this problem into two subproblems by setting (t + -4.5) equal to 1.658312395 and -1.658312395.Subproblem 1
t + -4.5 = 1.658312395 Simplifying t + -4.5 = 1.658312395 Reorder the terms: -4.5 + t = 1.658312395 Solving -4.5 + t = 1.658312395 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + t = 1.658312395 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + t = 1.658312395 + 4.5 t = 1.658312395 + 4.5 Combine like terms: 1.658312395 + 4.5 = 6.158312395 t = 6.158312395 Simplifying t = 6.158312395Subproblem 2
t + -4.5 = -1.658312395 Simplifying t + -4.5 = -1.658312395 Reorder the terms: -4.5 + t = -1.658312395 Solving -4.5 + t = -1.658312395 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + t = -1.658312395 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + t = -1.658312395 + 4.5 t = -1.658312395 + 4.5 Combine like terms: -1.658312395 + 4.5 = 2.841687605 t = 2.841687605 Simplifying t = 2.841687605Solution
The solution to the problem is based on the solutions from the subproblems. t = {6.158312395, 2.841687605}Solution
t = {6.158312395, 2.841687605}
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