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Simplifying 3t2 = 90 + 45t Solving 3t2 = 90 + 45t Solving for variable 't'. Reorder the terms: -90 + -45t + 3t2 = 90 + 45t + -90 + -45t Reorder the terms: -90 + -45t + 3t2 = 90 + -90 + 45t + -45t Combine like terms: 90 + -90 = 0 -90 + -45t + 3t2 = 0 + 45t + -45t -90 + -45t + 3t2 = 45t + -45t Combine like terms: 45t + -45t = 0 -90 + -45t + 3t2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-30 + -15t + t2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-30 + -15t + t2)' equal to zero and attempt to solve: Simplifying -30 + -15t + t2 = 0 Solving -30 + -15t + t2 = 0 Begin completing the square. Move the constant term to the right: Add '30' to each side of the equation. -30 + -15t + 30 + t2 = 0 + 30 Reorder the terms: -30 + 30 + -15t + t2 = 0 + 30 Combine like terms: -30 + 30 = 0 0 + -15t + t2 = 0 + 30 -15t + t2 = 0 + 30 Combine like terms: 0 + 30 = 30 -15t + t2 = 30 The t term is -15t. Take half its coefficient (-7.5). Square it (56.25) and add it to both sides. Add '56.25' to each side of the equation. -15t + 56.25 + t2 = 30 + 56.25 Reorder the terms: 56.25 + -15t + t2 = 30 + 56.25 Combine like terms: 30 + 56.25 = 86.25 56.25 + -15t + t2 = 86.25 Factor a perfect square on the left side: (t + -7.5)(t + -7.5) = 86.25 Calculate the square root of the right side: 9.287087811 Break this problem into two subproblems by setting (t + -7.5) equal to 9.287087811 and -9.287087811.Subproblem 1
t + -7.5 = 9.287087811 Simplifying t + -7.5 = 9.287087811 Reorder the terms: -7.5 + t = 9.287087811 Solving -7.5 + t = 9.287087811 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + t = 9.287087811 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + t = 9.287087811 + 7.5 t = 9.287087811 + 7.5 Combine like terms: 9.287087811 + 7.5 = 16.787087811 t = 16.787087811 Simplifying t = 16.787087811Subproblem 2
t + -7.5 = -9.287087811 Simplifying t + -7.5 = -9.287087811 Reorder the terms: -7.5 + t = -9.287087811 Solving -7.5 + t = -9.287087811 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + t = -9.287087811 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + t = -9.287087811 + 7.5 t = -9.287087811 + 7.5 Combine like terms: -9.287087811 + 7.5 = -1.787087811 t = -1.787087811 Simplifying t = -1.787087811Solution
The solution to the problem is based on the solutions from the subproblems. t = {16.787087811, -1.787087811}Solution
t = {16.787087811, -1.787087811}
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