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Simplifying 6 = -16t2 + 160t Reorder the terms: 6 = 160t + -16t2 Solving 6 = 160t + -16t2 Solving for variable 't'. Reorder the terms: 6 + -160t + 16t2 = 160t + -160t + -16t2 + 16t2 Combine like terms: 160t + -160t = 0 6 + -160t + 16t2 = 0 + -16t2 + 16t2 6 + -160t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 6 + -160t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(3 + -80t + 8t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(3 + -80t + 8t2)' equal to zero and attempt to solve: Simplifying 3 + -80t + 8t2 = 0 Solving 3 + -80t + 8t2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 0.375 + -10t + t2 = 0 Move the constant term to the right: Add '-0.375' to each side of the equation. 0.375 + -10t + -0.375 + t2 = 0 + -0.375 Reorder the terms: 0.375 + -0.375 + -10t + t2 = 0 + -0.375 Combine like terms: 0.375 + -0.375 = 0.000 0.000 + -10t + t2 = 0 + -0.375 -10t + t2 = 0 + -0.375 Combine like terms: 0 + -0.375 = -0.375 -10t + t2 = -0.375 The t term is -10t. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10t + 25 + t2 = -0.375 + 25 Reorder the terms: 25 + -10t + t2 = -0.375 + 25 Combine like terms: -0.375 + 25 = 24.625 25 + -10t + t2 = 24.625 Factor a perfect square on the left side: (t + -5)(t + -5) = 24.625 Calculate the square root of the right side: 4.96235831 Break this problem into two subproblems by setting (t + -5) equal to 4.96235831 and -4.96235831.Subproblem 1
t + -5 = 4.96235831 Simplifying t + -5 = 4.96235831 Reorder the terms: -5 + t = 4.96235831 Solving -5 + t = 4.96235831 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + t = 4.96235831 + 5 Combine like terms: -5 + 5 = 0 0 + t = 4.96235831 + 5 t = 4.96235831 + 5 Combine like terms: 4.96235831 + 5 = 9.96235831 t = 9.96235831 Simplifying t = 9.96235831Subproblem 2
t + -5 = -4.96235831 Simplifying t + -5 = -4.96235831 Reorder the terms: -5 + t = -4.96235831 Solving -5 + t = -4.96235831 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + t = -4.96235831 + 5 Combine like terms: -5 + 5 = 0 0 + t = -4.96235831 + 5 t = -4.96235831 + 5 Combine like terms: -4.96235831 + 5 = 0.03764169 t = 0.03764169 Simplifying t = 0.03764169Solution
The solution to the problem is based on the solutions from the subproblems. t = {9.96235831, 0.03764169}Solution
t = {9.96235831, 0.03764169}
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