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Simplifying 0 = -16t2 + 20t + 200 Reorder the terms: 0 = 200 + 20t + -16t2 Solving 0 = 200 + 20t + -16t2 Solving for variable 't'. Combine like terms: 0 + -200 = -200 -200 + -20t + 16t2 = 200 + 20t + -16t2 + -200 + -20t + 16t2 Reorder the terms: -200 + -20t + 16t2 = 200 + -200 + 20t + -20t + -16t2 + 16t2 Combine like terms: 200 + -200 = 0 -200 + -20t + 16t2 = 0 + 20t + -20t + -16t2 + 16t2 -200 + -20t + 16t2 = 20t + -20t + -16t2 + 16t2 Combine like terms: 20t + -20t = 0 -200 + -20t + 16t2 = 0 + -16t2 + 16t2 -200 + -20t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -200 + -20t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-50 + -5t + 4t2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-50 + -5t + 4t2)' equal to zero and attempt to solve: Simplifying -50 + -5t + 4t2 = 0 Solving -50 + -5t + 4t2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -12.5 + -1.25t + t2 = 0 Move the constant term to the right: Add '12.5' to each side of the equation. -12.5 + -1.25t + 12.5 + t2 = 0 + 12.5 Reorder the terms: -12.5 + 12.5 + -1.25t + t2 = 0 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + -1.25t + t2 = 0 + 12.5 -1.25t + t2 = 0 + 12.5 Combine like terms: 0 + 12.5 = 12.5 -1.25t + t2 = 12.5 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 = 12.5 + 0.390625 Reorder the terms: 0.390625 + -1.25t + t2 = 12.5 + 0.390625 Combine like terms: 12.5 + 0.390625 = 12.890625 0.390625 + -1.25t + t2 = 12.890625 Factor a perfect square on the left side: (t + -0.625)(t + -0.625) = 12.890625 Calculate the square root of the right side: 3.590351654 Break this problem into two subproblems by setting (t + -0.625) equal to 3.590351654 and -3.590351654.Subproblem 1
t + -0.625 = 3.590351654 Simplifying t + -0.625 = 3.590351654 Reorder the terms: -0.625 + t = 3.590351654 Solving -0.625 + t = 3.590351654 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 = 3.590351654 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + t = 3.590351654 + 0.625 t = 3.590351654 + 0.625 Combine like terms: 3.590351654 + 0.625 = 4.215351654 t = 4.215351654 Simplifying t = 4.215351654Subproblem 2
t + -0.625 = -3.590351654 Simplifying t + -0.625 = -3.590351654 Reorder the terms: -0.625 + t = -3.590351654 Solving -0.625 + t = -3.590351654 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 = -3.590351654 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + t = -3.590351654 + 0.625 t = -3.590351654 + 0.625 Combine like terms: -3.590351654 + 0.625 = -2.965351654 t = -2.965351654 Simplifying t = -2.965351654Solution
The solution to the problem is based on the solutions from the subproblems. t = {4.215351654, -2.965351654}Solution
t = {4.215351654, -2.965351654}
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