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Simplifying 0 = -16t2 + -60t + 360 Reorder the terms: 0 = 360 + -60t + -16t2 Solving 0 = 360 + -60t + -16t2 Solving for variable 't'. Combine like terms: 0 + -360 = -360 -360 + 60t + 16t2 = 360 + -60t + -16t2 + -360 + 60t + 16t2 Reorder the terms: -360 + 60t + 16t2 = 360 + -360 + -60t + 60t + -16t2 + 16t2 Combine like terms: 360 + -360 = 0 -360 + 60t + 16t2 = 0 + -60t + 60t + -16t2 + 16t2 -360 + 60t + 16t2 = -60t + 60t + -16t2 + 16t2 Combine like terms: -60t + 60t = 0 -360 + 60t + 16t2 = 0 + -16t2 + 16t2 -360 + 60t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -360 + 60t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-90 + 15t + 4t2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-90 + 15t + 4t2)' equal to zero and attempt to solve: Simplifying -90 + 15t + 4t2 = 0 Solving -90 + 15t + 4t2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -22.5 + 3.75t + t2 = 0 Move the constant term to the right: Add '22.5' to each side of the equation. -22.5 + 3.75t + 22.5 + t2 = 0 + 22.5 Reorder the terms: -22.5 + 22.5 + 3.75t + t2 = 0 + 22.5 Combine like terms: -22.5 + 22.5 = 0.0 0.0 + 3.75t + t2 = 0 + 22.5 3.75t + t2 = 0 + 22.5 Combine like terms: 0 + 22.5 = 22.5 3.75t + t2 = 22.5 The t term is 3.75t. Take half its coefficient (1.875). Square it (3.515625) and add it to both sides. Add '3.515625' to each side of the equation. 3.75t + 3.515625 + t2 = 22.5 + 3.515625 Reorder the terms: 3.515625 + 3.75t + t2 = 22.5 + 3.515625 Combine like terms: 22.5 + 3.515625 = 26.015625 3.515625 + 3.75t + t2 = 26.015625 Factor a perfect square on the left side: (t + 1.875)(t + 1.875) = 26.015625 Calculate the square root of the right side: 5.100551441 Break this problem into two subproblems by setting (t + 1.875) equal to 5.100551441 and -5.100551441.Subproblem 1
t + 1.875 = 5.100551441 Simplifying t + 1.875 = 5.100551441 Reorder the terms: 1.875 + t = 5.100551441 Solving 1.875 + t = 5.100551441 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-1.875' to each side of the equation. 1.875 + -1.875 + t = 5.100551441 + -1.875 Combine like terms: 1.875 + -1.875 = 0.000 0.000 + t = 5.100551441 + -1.875 t = 5.100551441 + -1.875 Combine like terms: 5.100551441 + -1.875 = 3.225551441 t = 3.225551441 Simplifying t = 3.225551441Subproblem 2
t + 1.875 = -5.100551441 Simplifying t + 1.875 = -5.100551441 Reorder the terms: 1.875 + t = -5.100551441 Solving 1.875 + t = -5.100551441 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-1.875' to each side of the equation. 1.875 + -1.875 + t = -5.100551441 + -1.875 Combine like terms: 1.875 + -1.875 = 0.000 0.000 + t = -5.100551441 + -1.875 t = -5.100551441 + -1.875 Combine like terms: -5.100551441 + -1.875 = -6.975551441 t = -6.975551441 Simplifying t = -6.975551441Solution
The solution to the problem is based on the solutions from the subproblems. t = {3.225551441, -6.975551441}Solution
t = {3.225551441, -6.975551441}
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