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Simplifying -16t2 + 144t + 340 = 0 Reorder the terms: 340 + 144t + -16t2 = 0 Solving 340 + 144t + -16t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '4'. 4(85 + 36t + -4t2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(85 + 36t + -4t2)' equal to zero and attempt to solve: Simplifying 85 + 36t + -4t2 = 0 Solving 85 + 36t + -4t2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -21.25 + -9t + t2 = 0 Move the constant term to the right: Add '21.25' to each side of the equation. -21.25 + -9t + 21.25 + t2 = 0 + 21.25 Reorder the terms: -21.25 + 21.25 + -9t + t2 = 0 + 21.25 Combine like terms: -21.25 + 21.25 = 0.00 0.00 + -9t + t2 = 0 + 21.25 -9t + t2 = 0 + 21.25 Combine like terms: 0 + 21.25 = 21.25 -9t + t2 = 21.25 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 = 21.25 + 20.25 Reorder the terms: 20.25 + -9t + t2 = 21.25 + 20.25 Combine like terms: 21.25 + 20.25 = 41.5 20.25 + -9t + t2 = 41.5 Factor a perfect square on the left side: (t + -4.5)(t + -4.5) = 41.5 Calculate the square root of the right side: 6.442049363 Break this problem into two subproblems by setting (t + -4.5) equal to 6.442049363 and -6.442049363.Subproblem 1
t + -4.5 = 6.442049363 Simplifying t + -4.5 = 6.442049363 Reorder the terms: -4.5 + t = 6.442049363 Solving -4.5 + t = 6.442049363 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 = 6.442049363 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + t = 6.442049363 + 4.5 t = 6.442049363 + 4.5 Combine like terms: 6.442049363 + 4.5 = 10.942049363 t = 10.942049363 Simplifying t = 10.942049363Subproblem 2
t + -4.5 = -6.442049363 Simplifying t + -4.5 = -6.442049363 Reorder the terms: -4.5 + t = -6.442049363 Solving -4.5 + t = -6.442049363 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 = -6.442049363 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + t = -6.442049363 + 4.5 t = -6.442049363 + 4.5 Combine like terms: -6.442049363 + 4.5 = -1.942049363 t = -1.942049363 Simplifying t = -1.942049363Solution
The solution to the problem is based on the solutions from the subproblems. t = {10.942049363, -1.942049363}Solution
t = {10.942049363, -1.942049363}
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