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Simplifying -16t2 + 92t + 160 = 0 Reorder the terms: 160 + 92t + -16t2 = 0 Solving 160 + 92t + -16t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '4'. 4(40 + 23t + -4t2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(40 + 23t + -4t2)' equal to zero and attempt to solve: Simplifying 40 + 23t + -4t2 = 0 Solving 40 + 23t + -4t2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -10 + -5.75t + t2 = 0 Move the constant term to the right: Add '10' to each side of the equation. -10 + -5.75t + 10 + t2 = 0 + 10 Reorder the terms: -10 + 10 + -5.75t + t2 = 0 + 10 Combine like terms: -10 + 10 = 0 0 + -5.75t + t2 = 0 + 10 -5.75t + t2 = 0 + 10 Combine like terms: 0 + 10 = 10 -5.75t + t2 = 10 The t term is -5.75t. Take half its coefficient (-2.875). Square it (8.265625) and add it to both sides. Add '8.265625' to each side of the equation. -5.75t + 8.265625 + t2 = 10 + 8.265625 Reorder the terms: 8.265625 + -5.75t + t2 = 10 + 8.265625 Combine like terms: 10 + 8.265625 = 18.265625 8.265625 + -5.75t + t2 = 18.265625 Factor a perfect square on the left side: (t + -2.875)(t + -2.875) = 18.265625 Calculate the square root of the right side: 4.273830249 Break this problem into two subproblems by setting (t + -2.875) equal to 4.273830249 and -4.273830249.Subproblem 1
t + -2.875 = 4.273830249 Simplifying t + -2.875 = 4.273830249 Reorder the terms: -2.875 + t = 4.273830249 Solving -2.875 + t = 4.273830249 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.875' to each side of the equation. -2.875 + 2.875 + t = 4.273830249 + 2.875 Combine like terms: -2.875 + 2.875 = 0.000 0.000 + t = 4.273830249 + 2.875 t = 4.273830249 + 2.875 Combine like terms: 4.273830249 + 2.875 = 7.148830249 t = 7.148830249 Simplifying t = 7.148830249Subproblem 2
t + -2.875 = -4.273830249 Simplifying t + -2.875 = -4.273830249 Reorder the terms: -2.875 + t = -4.273830249 Solving -2.875 + t = -4.273830249 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.875' to each side of the equation. -2.875 + 2.875 + t = -4.273830249 + 2.875 Combine like terms: -2.875 + 2.875 = 0.000 0.000 + t = -4.273830249 + 2.875 t = -4.273830249 + 2.875 Combine like terms: -4.273830249 + 2.875 = -1.398830249 t = -1.398830249 Simplifying t = -1.398830249Solution
The solution to the problem is based on the solutions from the subproblems. t = {7.148830249, -1.398830249}Solution
t = {7.148830249, -1.398830249}
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