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Simplifying 75 = 150 + -200t + 50t2 Solving 75 = 150 + -200t + 50t2 Solving for variable 't'. Combine like terms: 75 + -150 = -75 -75 + 200t + -50t2 = 150 + -200t + 50t2 + -150 + 200t + -50t2 Reorder the terms: -75 + 200t + -50t2 = 150 + -150 + -200t + 200t + 50t2 + -50t2 Combine like terms: 150 + -150 = 0 -75 + 200t + -50t2 = 0 + -200t + 200t + 50t2 + -50t2 -75 + 200t + -50t2 = -200t + 200t + 50t2 + -50t2 Combine like terms: -200t + 200t = 0 -75 + 200t + -50t2 = 0 + 50t2 + -50t2 -75 + 200t + -50t2 = 50t2 + -50t2 Combine like terms: 50t2 + -50t2 = 0 -75 + 200t + -50t2 = 0 Factor out the Greatest Common Factor (GCF), '25'. 25(-3 + 8t + -2t2) = 0 Ignore the factor 25.Subproblem 1
Set the factor '(-3 + 8t + -2t2)' equal to zero and attempt to solve: Simplifying -3 + 8t + -2t2 = 0 Solving -3 + 8t + -2t2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. 1.5 + -4t + t2 = 0 Move the constant term to the right: Add '-1.5' to each side of the equation. 1.5 + -4t + -1.5 + t2 = 0 + -1.5 Reorder the terms: 1.5 + -1.5 + -4t + t2 = 0 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + -4t + t2 = 0 + -1.5 -4t + t2 = 0 + -1.5 Combine like terms: 0 + -1.5 = -1.5 -4t + t2 = -1.5 The t term is -4t. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4t + 4 + t2 = -1.5 + 4 Reorder the terms: 4 + -4t + t2 = -1.5 + 4 Combine like terms: -1.5 + 4 = 2.5 4 + -4t + t2 = 2.5 Factor a perfect square on the left side: (t + -2)(t + -2) = 2.5 Calculate the square root of the right side: 1.58113883 Break this problem into two subproblems by setting (t + -2) equal to 1.58113883 and -1.58113883.Subproblem 1
t + -2 = 1.58113883 Simplifying t + -2 = 1.58113883 Reorder the terms: -2 + t = 1.58113883 Solving -2 + t = 1.58113883 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + t = 1.58113883 + 2 Combine like terms: -2 + 2 = 0 0 + t = 1.58113883 + 2 t = 1.58113883 + 2 Combine like terms: 1.58113883 + 2 = 3.58113883 t = 3.58113883 Simplifying t = 3.58113883Subproblem 2
t + -2 = -1.58113883 Simplifying t + -2 = -1.58113883 Reorder the terms: -2 + t = -1.58113883 Solving -2 + t = -1.58113883 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + t = -1.58113883 + 2 Combine like terms: -2 + 2 = 0 0 + t = -1.58113883 + 2 t = -1.58113883 + 2 Combine like terms: -1.58113883 + 2 = 0.41886117 t = 0.41886117 Simplifying t = 0.41886117Solution
The solution to the problem is based on the solutions from the subproblems. t = {3.58113883, 0.41886117}Solution
t = {3.58113883, 0.41886117}
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