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Simplifying 5t2 + -350t + 600 = 0 Reorder the terms: 600 + -350t + 5t2 = 0 Solving 600 + -350t + 5t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '5'. 5(120 + -70t + t2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(120 + -70t + t2)' equal to zero and attempt to solve: Simplifying 120 + -70t + t2 = 0 Solving 120 + -70t + t2 = 0 Begin completing the square. Move the constant term to the right: Add '-120' to each side of the equation. 120 + -70t + -120 + t2 = 0 + -120 Reorder the terms: 120 + -120 + -70t + t2 = 0 + -120 Combine like terms: 120 + -120 = 0 0 + -70t + t2 = 0 + -120 -70t + t2 = 0 + -120 Combine like terms: 0 + -120 = -120 -70t + t2 = -120 The t term is -70t. Take half its coefficient (-35). Square it (1225) and add it to both sides. Add '1225' to each side of the equation. -70t + 1225 + t2 = -120 + 1225 Reorder the terms: 1225 + -70t + t2 = -120 + 1225 Combine like terms: -120 + 1225 = 1105 1225 + -70t + t2 = 1105 Factor a perfect square on the left side: (t + -35)(t + -35) = 1105 Calculate the square root of the right side: 33.241540277 Break this problem into two subproblems by setting (t + -35) equal to 33.241540277 and -33.241540277.Subproblem 1
t + -35 = 33.241540277 Simplifying t + -35 = 33.241540277 Reorder the terms: -35 + t = 33.241540277 Solving -35 + t = 33.241540277 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '35' to each side of the equation. -35 + 35 + t = 33.241540277 + 35 Combine like terms: -35 + 35 = 0 0 + t = 33.241540277 + 35 t = 33.241540277 + 35 Combine like terms: 33.241540277 + 35 = 68.241540277 t = 68.241540277 Simplifying t = 68.241540277Subproblem 2
t + -35 = -33.241540277 Simplifying t + -35 = -33.241540277 Reorder the terms: -35 + t = -33.241540277 Solving -35 + t = -33.241540277 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '35' to each side of the equation. -35 + 35 + t = -33.241540277 + 35 Combine like terms: -35 + 35 = 0 0 + t = -33.241540277 + 35 t = -33.241540277 + 35 Combine like terms: -33.241540277 + 35 = 1.758459723 t = 1.758459723 Simplifying t = 1.758459723Solution
The solution to the problem is based on the solutions from the subproblems. t = {68.241540277, 1.758459723}Solution
t = {68.241540277, 1.758459723}
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