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Simplifying 200 = 256t + -16t2 Solving 200 = 256t + -16t2 Solving for variable 't'. Reorder the terms: 200 + -256t + 16t2 = 256t + -256t + -16t2 + 16t2 Combine like terms: 256t + -256t = 0 200 + -256t + 16t2 = 0 + -16t2 + 16t2 200 + -256t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 200 + -256t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '8'. 8(25 + -32t + 2t2) = 0 Ignore the factor 8.Subproblem 1
Set the factor '(25 + -32t + 2t2)' equal to zero and attempt to solve: Simplifying 25 + -32t + 2t2 = 0 Solving 25 + -32t + 2t2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 12.5 + -16t + t2 = 0 Move the constant term to the right: Add '-12.5' to each side of the equation. 12.5 + -16t + -12.5 + t2 = 0 + -12.5 Reorder the terms: 12.5 + -12.5 + -16t + t2 = 0 + -12.5 Combine like terms: 12.5 + -12.5 = 0.0 0.0 + -16t + t2 = 0 + -12.5 -16t + t2 = 0 + -12.5 Combine like terms: 0 + -12.5 = -12.5 -16t + t2 = -12.5 The t term is -16t. Take half its coefficient (-8). Square it (64) and add it to both sides. Add '64' to each side of the equation. -16t + 64 + t2 = -12.5 + 64 Reorder the terms: 64 + -16t + t2 = -12.5 + 64 Combine like terms: -12.5 + 64 = 51.5 64 + -16t + t2 = 51.5 Factor a perfect square on the left side: (t + -8)(t + -8) = 51.5 Calculate the square root of the right side: 7.176350047 Break this problem into two subproblems by setting (t + -8) equal to 7.176350047 and -7.176350047.Subproblem 1
t + -8 = 7.176350047 Simplifying t + -8 = 7.176350047 Reorder the terms: -8 + t = 7.176350047 Solving -8 + t = 7.176350047 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + t = 7.176350047 + 8 Combine like terms: -8 + 8 = 0 0 + t = 7.176350047 + 8 t = 7.176350047 + 8 Combine like terms: 7.176350047 + 8 = 15.176350047 t = 15.176350047 Simplifying t = 15.176350047Subproblem 2
t + -8 = -7.176350047 Simplifying t + -8 = -7.176350047 Reorder the terms: -8 + t = -7.176350047 Solving -8 + t = -7.176350047 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + t = -7.176350047 + 8 Combine like terms: -8 + 8 = 0 0 + t = -7.176350047 + 8 t = -7.176350047 + 8 Combine like terms: -7.176350047 + 8 = 0.823649953 t = 0.823649953 Simplifying t = 0.823649953Solution
The solution to the problem is based on the solutions from the subproblems. t = {15.176350047, 0.823649953}Solution
t = {15.176350047, 0.823649953}
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