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Simplifying 400 = -16t2 + 180t + 0 Reorder the terms: 400 = 0 + 180t + -16t2 Remove the zero: 400 = 180t + -16t2 Solving 400 = 180t + -16t2 Solving for variable 't'. Reorder the terms: 400 + -180t + 16t2 = 180t + -180t + -16t2 + 16t2 Combine like terms: 180t + -180t = 0 400 + -180t + 16t2 = 0 + -16t2 + 16t2 400 + -180t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 400 + -180t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(100 + -45t + 4t2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(100 + -45t + 4t2)' equal to zero and attempt to solve: Simplifying 100 + -45t + 4t2 = 0 Solving 100 + -45t + 4t2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 25 + -11.25t + t2 = 0 Move the constant term to the right: Add '-25' to each side of the equation. 25 + -11.25t + -25 + t2 = 0 + -25 Reorder the terms: 25 + -25 + -11.25t + t2 = 0 + -25 Combine like terms: 25 + -25 = 0 0 + -11.25t + t2 = 0 + -25 -11.25t + t2 = 0 + -25 Combine like terms: 0 + -25 = -25 -11.25t + t2 = -25 The t term is -11.25t. Take half its coefficient (-5.625). Square it (31.640625) and add it to both sides. Add '31.640625' to each side of the equation. -11.25t + 31.640625 + t2 = -25 + 31.640625 Reorder the terms: 31.640625 + -11.25t + t2 = -25 + 31.640625 Combine like terms: -25 + 31.640625 = 6.640625 31.640625 + -11.25t + t2 = 6.640625 Factor a perfect square on the left side: (t + -5.625)(t + -5.625) = 6.640625 Calculate the square root of the right side: 2.576941016 Break this problem into two subproblems by setting (t + -5.625) equal to 2.576941016 and -2.576941016.Subproblem 1
t + -5.625 = 2.576941016 Simplifying t + -5.625 = 2.576941016 Reorder the terms: -5.625 + t = 2.576941016 Solving -5.625 + t = 2.576941016 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '5.625' to each side of the equation. -5.625 + 5.625 + t = 2.576941016 + 5.625 Combine like terms: -5.625 + 5.625 = 0.000 0.000 + t = 2.576941016 + 5.625 t = 2.576941016 + 5.625 Combine like terms: 2.576941016 + 5.625 = 8.201941016 t = 8.201941016 Simplifying t = 8.201941016Subproblem 2
t + -5.625 = -2.576941016 Simplifying t + -5.625 = -2.576941016 Reorder the terms: -5.625 + t = -2.576941016 Solving -5.625 + t = -2.576941016 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '5.625' to each side of the equation. -5.625 + 5.625 + t = -2.576941016 + 5.625 Combine like terms: -5.625 + 5.625 = 0.000 0.000 + t = -2.576941016 + 5.625 t = -2.576941016 + 5.625 Combine like terms: -2.576941016 + 5.625 = 3.048058984 t = 3.048058984 Simplifying t = 3.048058984Solution
The solution to the problem is based on the solutions from the subproblems. t = {8.201941016, 3.048058984}Solution
t = {8.201941016, 3.048058984}
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