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Simplifying 20t = -16t2 + 20 Reorder the terms: 20t = 20 + -16t2 Solving 20t = 20 + -16t2 Solving for variable 't'. Reorder the terms: -20 + 20t + 16t2 = 20 + -16t2 + -20 + 16t2 Reorder the terms: -20 + 20t + 16t2 = 20 + -20 + -16t2 + 16t2 Combine like terms: 20 + -20 = 0 -20 + 20t + 16t2 = 0 + -16t2 + 16t2 -20 + 20t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -20 + 20t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-5 + 5t + 4t2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-5 + 5t + 4t2)' equal to zero and attempt to solve: Simplifying -5 + 5t + 4t2 = 0 Solving -5 + 5t + 4t2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -1.25 + 1.25t + t2 = 0 Move the constant term to the right: Add '1.25' to each side of the equation. -1.25 + 1.25t + 1.25 + t2 = 0 + 1.25 Reorder the terms: -1.25 + 1.25 + 1.25t + t2 = 0 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + 1.25t + t2 = 0 + 1.25 1.25t + t2 = 0 + 1.25 Combine like terms: 0 + 1.25 = 1.25 1.25t + t2 = 1.25 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 = 1.25 + 0.390625 Reorder the terms: 0.390625 + 1.25t + t2 = 1.25 + 0.390625 Combine like terms: 1.25 + 0.390625 = 1.640625 0.390625 + 1.25t + t2 = 1.640625 Factor a perfect square on the left side: (t + 0.625)(t + 0.625) = 1.640625 Calculate the square root of the right side: 1.280868846 Break this problem into two subproblems by setting (t + 0.625) equal to 1.280868846 and -1.280868846.Subproblem 1
t + 0.625 = 1.280868846 Simplifying t + 0.625 = 1.280868846 Reorder the terms: 0.625 + t = 1.280868846 Solving 0.625 + t = 1.280868846 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 = 1.280868846 + -0.625 Combine like terms: 0.625 + -0.625 = 0.000 0.000 + t = 1.280868846 + -0.625 t = 1.280868846 + -0.625 Combine like terms: 1.280868846 + -0.625 = 0.655868846 t = 0.655868846 Simplifying t = 0.655868846Subproblem 2
t + 0.625 = -1.280868846 Simplifying t + 0.625 = -1.280868846 Reorder the terms: 0.625 + t = -1.280868846 Solving 0.625 + t = -1.280868846 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 = -1.280868846 + -0.625 Combine like terms: 0.625 + -0.625 = 0.000 0.000 + t = -1.280868846 + -0.625 t = -1.280868846 + -0.625 Combine like terms: -1.280868846 + -0.625 = -1.905868846 t = -1.905868846 Simplifying t = -1.905868846Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.655868846, -1.905868846}Solution
t = {0.655868846, -1.905868846}
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