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Simplifying -16t2 + 150t + 64 = 0 Reorder the terms: 64 + 150t + -16t2 = 0 Solving 64 + 150t + -16t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '2'. 2(32 + 75t + -8t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(32 + 75t + -8t2)' equal to zero and attempt to solve: Simplifying 32 + 75t + -8t2 = 0 Solving 32 + 75t + -8t2 = 0 Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. -4 + -9.375t + t2 = 0 Move the constant term to the right: Add '4' to each side of the equation. -4 + -9.375t + 4 + t2 = 0 + 4 Reorder the terms: -4 + 4 + -9.375t + t2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -9.375t + t2 = 0 + 4 -9.375t + t2 = 0 + 4 Combine like terms: 0 + 4 = 4 -9.375t + t2 = 4 The t term is -9.375t. Take half its coefficient (-4.6875). Square it (21.97265625) and add it to both sides. Add '21.97265625' to each side of the equation. -9.375t + 21.97265625 + t2 = 4 + 21.97265625 Reorder the terms: 21.97265625 + -9.375t + t2 = 4 + 21.97265625 Combine like terms: 4 + 21.97265625 = 25.97265625 21.97265625 + -9.375t + t2 = 25.97265625 Factor a perfect square on the left side: (t + -4.6875)(t + -4.6875) = 25.97265625 Calculate the square root of the right side: 5.096337533 Break this problem into two subproblems by setting (t + -4.6875) equal to 5.096337533 and -5.096337533.Subproblem 1
t + -4.6875 = 5.096337533 Simplifying t + -4.6875 = 5.096337533 Reorder the terms: -4.6875 + t = 5.096337533 Solving -4.6875 + t = 5.096337533 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '4.6875' to each side of the equation. -4.6875 + 4.6875 + t = 5.096337533 + 4.6875 Combine like terms: -4.6875 + 4.6875 = 0.0000 0.0000 + t = 5.096337533 + 4.6875 t = 5.096337533 + 4.6875 Combine like terms: 5.096337533 + 4.6875 = 9.783837533 t = 9.783837533 Simplifying t = 9.783837533Subproblem 2
t + -4.6875 = -5.096337533 Simplifying t + -4.6875 = -5.096337533 Reorder the terms: -4.6875 + t = -5.096337533 Solving -4.6875 + t = -5.096337533 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '4.6875' to each side of the equation. -4.6875 + 4.6875 + t = -5.096337533 + 4.6875 Combine like terms: -4.6875 + 4.6875 = 0.0000 0.0000 + t = -5.096337533 + 4.6875 t = -5.096337533 + 4.6875 Combine like terms: -5.096337533 + 4.6875 = -0.408837533 t = -0.408837533 Simplifying t = -0.408837533Solution
The solution to the problem is based on the solutions from the subproblems. t = {9.783837533, -0.408837533}Solution
t = {9.783837533, -0.408837533}
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