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Simplifying 34 = 100t + -16t2 Solving 34 = 100t + -16t2 Solving for variable 't'. Reorder the terms: 34 + -100t + 16t2 = 100t + -100t + -16t2 + 16t2 Combine like terms: 100t + -100t = 0 34 + -100t + 16t2 = 0 + -16t2 + 16t2 34 + -100t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 34 + -100t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(17 + -50t + 8t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(17 + -50t + 8t2)' equal to zero and attempt to solve: Simplifying 17 + -50t + 8t2 = 0 Solving 17 + -50t + 8t2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 2.125 + -6.25t + t2 = 0 Move the constant term to the right: Add '-2.125' to each side of the equation. 2.125 + -6.25t + -2.125 + t2 = 0 + -2.125 Reorder the terms: 2.125 + -2.125 + -6.25t + t2 = 0 + -2.125 Combine like terms: 2.125 + -2.125 = 0.000 0.000 + -6.25t + t2 = 0 + -2.125 -6.25t + t2 = 0 + -2.125 Combine like terms: 0 + -2.125 = -2.125 -6.25t + t2 = -2.125 The t term is -6.25t. Take half its coefficient (-3.125). Square it (9.765625) and add it to both sides. Add '9.765625' to each side of the equation. -6.25t + 9.765625 + t2 = -2.125 + 9.765625 Reorder the terms: 9.765625 + -6.25t + t2 = -2.125 + 9.765625 Combine like terms: -2.125 + 9.765625 = 7.640625 9.765625 + -6.25t + t2 = 7.640625 Factor a perfect square on the left side: (t + -3.125)(t + -3.125) = 7.640625 Calculate the square root of the right side: 2.764168048 Break this problem into two subproblems by setting (t + -3.125) equal to 2.764168048 and -2.764168048.Subproblem 1
t + -3.125 = 2.764168048 Simplifying t + -3.125 = 2.764168048 Reorder the terms: -3.125 + t = 2.764168048 Solving -3.125 + t = 2.764168048 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3.125' to each side of the equation. -3.125 + 3.125 + t = 2.764168048 + 3.125 Combine like terms: -3.125 + 3.125 = 0.000 0.000 + t = 2.764168048 + 3.125 t = 2.764168048 + 3.125 Combine like terms: 2.764168048 + 3.125 = 5.889168048 t = 5.889168048 Simplifying t = 5.889168048Subproblem 2
t + -3.125 = -2.764168048 Simplifying t + -3.125 = -2.764168048 Reorder the terms: -3.125 + t = -2.764168048 Solving -3.125 + t = -2.764168048 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3.125' to each side of the equation. -3.125 + 3.125 + t = -2.764168048 + 3.125 Combine like terms: -3.125 + 3.125 = 0.000 0.000 + t = -2.764168048 + 3.125 t = -2.764168048 + 3.125 Combine like terms: -2.764168048 + 3.125 = 0.360831952 t = 0.360831952 Simplifying t = 0.360831952Solution
The solution to the problem is based on the solutions from the subproblems. t = {5.889168048, 0.360831952}Solution
t = {5.889168048, 0.360831952}
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