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Simplifying 0 = -16t2 + 220t + 100 Reorder the terms: 0 = 100 + 220t + -16t2 Solving 0 = 100 + 220t + -16t2 Solving for variable 't'. Combine like terms: 0 + -100 = -100 -100 + -220t + 16t2 = 100 + 220t + -16t2 + -100 + -220t + 16t2 Reorder the terms: -100 + -220t + 16t2 = 100 + -100 + 220t + -220t + -16t2 + 16t2 Combine like terms: 100 + -100 = 0 -100 + -220t + 16t2 = 0 + 220t + -220t + -16t2 + 16t2 -100 + -220t + 16t2 = 220t + -220t + -16t2 + 16t2 Combine like terms: 220t + -220t = 0 -100 + -220t + 16t2 = 0 + -16t2 + 16t2 -100 + -220t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -100 + -220t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-25 + -55t + 4t2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-25 + -55t + 4t2)' equal to zero and attempt to solve: Simplifying -25 + -55t + 4t2 = 0 Solving -25 + -55t + 4t2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -6.25 + -13.75t + t2 = 0 Move the constant term to the right: Add '6.25' to each side of the equation. -6.25 + -13.75t + 6.25 + t2 = 0 + 6.25 Reorder the terms: -6.25 + 6.25 + -13.75t + t2 = 0 + 6.25 Combine like terms: -6.25 + 6.25 = 0.00 0.00 + -13.75t + t2 = 0 + 6.25 -13.75t + t2 = 0 + 6.25 Combine like terms: 0 + 6.25 = 6.25 -13.75t + t2 = 6.25 The t term is -13.75t. Take half its coefficient (-6.875). Square it (47.265625) and add it to both sides. Add '47.265625' to each side of the equation. -13.75t + 47.265625 + t2 = 6.25 + 47.265625 Reorder the terms: 47.265625 + -13.75t + t2 = 6.25 + 47.265625 Combine like terms: 6.25 + 47.265625 = 53.515625 47.265625 + -13.75t + t2 = 53.515625 Factor a perfect square on the left side: (t + -6.875)(t + -6.875) = 53.515625 Calculate the square root of the right side: 7.315437444 Break this problem into two subproblems by setting (t + -6.875) equal to 7.315437444 and -7.315437444.Subproblem 1
t + -6.875 = 7.315437444 Simplifying t + -6.875 = 7.315437444 Reorder the terms: -6.875 + t = 7.315437444 Solving -6.875 + t = 7.315437444 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '6.875' to each side of the equation. -6.875 + 6.875 + t = 7.315437444 + 6.875 Combine like terms: -6.875 + 6.875 = 0.000 0.000 + t = 7.315437444 + 6.875 t = 7.315437444 + 6.875 Combine like terms: 7.315437444 + 6.875 = 14.190437444 t = 14.190437444 Simplifying t = 14.190437444Subproblem 2
t + -6.875 = -7.315437444 Simplifying t + -6.875 = -7.315437444 Reorder the terms: -6.875 + t = -7.315437444 Solving -6.875 + t = -7.315437444 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '6.875' to each side of the equation. -6.875 + 6.875 + t = -7.315437444 + 6.875 Combine like terms: -6.875 + 6.875 = 0.000 0.000 + t = -7.315437444 + 6.875 t = -7.315437444 + 6.875 Combine like terms: -7.315437444 + 6.875 = -0.440437444 t = -0.440437444 Simplifying t = -0.440437444Solution
The solution to the problem is based on the solutions from the subproblems. t = {14.190437444, -0.440437444}Solution
t = {14.190437444, -0.440437444}
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