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Simplifying 0 = -16t2 + -20t + 100 Reorder the terms: 0 = 100 + -20t + -16t2 Solving 0 = 100 + -20t + -16t2 Solving for variable 't'. Combine like terms: 0 + -100 = -100 -100 + 20t + 16t2 = 100 + -20t + -16t2 + -100 + 20t + 16t2 Reorder the terms: -100 + 20t + 16t2 = 100 + -100 + -20t + 20t + -16t2 + 16t2 Combine like terms: 100 + -100 = 0 -100 + 20t + 16t2 = 0 + -20t + 20t + -16t2 + 16t2 -100 + 20t + 16t2 = -20t + 20t + -16t2 + 16t2 Combine like terms: -20t + 20t = 0 -100 + 20t + 16t2 = 0 + -16t2 + 16t2 -100 + 20t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -100 + 20t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-25 + 5t + 4t2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-25 + 5t + 4t2)' equal to zero and attempt to solve: Simplifying -25 + 5t + 4t2 = 0 Solving -25 + 5t + 4t2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -6.25 + 1.25t + t2 = 0 Move the constant term to the right: Add '6.25' to each side of the equation. -6.25 + 1.25t + 6.25 + t2 = 0 + 6.25 Reorder the terms: -6.25 + 6.25 + 1.25t + t2 = 0 + 6.25 Combine like terms: -6.25 + 6.25 = 0.00 0.00 + 1.25t + t2 = 0 + 6.25 1.25t + t2 = 0 + 6.25 Combine like terms: 0 + 6.25 = 6.25 1.25t + t2 = 6.25 The t term is 1.25t. Take half its coefficient (0.625). Square it (0.390625) and add it to both sides. Add '0.390625' to each side of the equation. 1.25t + 0.390625 + t2 = 6.25 + 0.390625 Reorder the terms: 0.390625 + 1.25t + t2 = 6.25 + 0.390625 Combine like terms: 6.25 + 0.390625 = 6.640625 0.390625 + 1.25t + t2 = 6.640625 Factor a perfect square on the left side: (t + 0.625)(t + 0.625) = 6.640625 Calculate the square root of the right side: 2.576941016 Break this problem into two subproblems by setting (t + 0.625) equal to 2.576941016 and -2.576941016.Subproblem 1
t + 0.625 = 2.576941016 Simplifying t + 0.625 = 2.576941016 Reorder the terms: 0.625 + t = 2.576941016 Solving 0.625 + t = 2.576941016 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.625' to each side of the equation. 0.625 + -0.625 + t = 2.576941016 + -0.625 Combine like terms: 0.625 + -0.625 = 0.000 0.000 + t = 2.576941016 + -0.625 t = 2.576941016 + -0.625 Combine like terms: 2.576941016 + -0.625 = 1.951941016 t = 1.951941016 Simplifying t = 1.951941016Subproblem 2
t + 0.625 = -2.576941016 Simplifying t + 0.625 = -2.576941016 Reorder the terms: 0.625 + t = -2.576941016 Solving 0.625 + t = -2.576941016 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.625' to each side of the equation. 0.625 + -0.625 + t = -2.576941016 + -0.625 Combine like terms: 0.625 + -0.625 = 0.000 0.000 + t = -2.576941016 + -0.625 t = -2.576941016 + -0.625 Combine like terms: -2.576941016 + -0.625 = -3.201941016 t = -3.201941016 Simplifying t = -3.201941016Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.951941016, -3.201941016}Solution
t = {1.951941016, -3.201941016}
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