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Simplifying 150 = 50t2 + 200t Reorder the terms: 150 = 200t + 50t2 Solving 150 = 200t + 50t2 Solving for variable 't'. Reorder the terms: 150 + -200t + -50t2 = 200t + -200t + 50t2 + -50t2 Combine like terms: 200t + -200t = 0 150 + -200t + -50t2 = 0 + 50t2 + -50t2 150 + -200t + -50t2 = 50t2 + -50t2 Combine like terms: 50t2 + -50t2 = 0 150 + -200t + -50t2 = 0 Factor out the Greatest Common Factor (GCF), '50'. 50(3 + -4t + -1t2) = 0 Ignore the factor 50.Subproblem 1
Set the factor '(3 + -4t + -1t2)' equal to zero and attempt to solve: Simplifying 3 + -4t + -1t2 = 0 Solving 3 + -4t + -1t2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -3 + 4t + t2 = 0 Move the constant term to the right: Add '3' to each side of the equation. -3 + 4t + 3 + t2 = 0 + 3 Reorder the terms: -3 + 3 + 4t + t2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + 4t + t2 = 0 + 3 4t + t2 = 0 + 3 Combine like terms: 0 + 3 = 3 4t + t2 = 3 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 = 3 + 4 Reorder the terms: 4 + 4t + t2 = 3 + 4 Combine like terms: 3 + 4 = 7 4 + 4t + t2 = 7 Factor a perfect square on the left side: (t + 2)(t + 2) = 7 Calculate the square root of the right side: 2.645751311 Break this problem into two subproblems by setting (t + 2) equal to 2.645751311 and -2.645751311.Subproblem 1
t + 2 = 2.645751311 Simplifying t + 2 = 2.645751311 Reorder the terms: 2 + t = 2.645751311 Solving 2 + t = 2.645751311 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 = 2.645751311 + -2 Combine like terms: 2 + -2 = 0 0 + t = 2.645751311 + -2 t = 2.645751311 + -2 Combine like terms: 2.645751311 + -2 = 0.645751311 t = 0.645751311 Simplifying t = 0.645751311Subproblem 2
t + 2 = -2.645751311 Simplifying t + 2 = -2.645751311 Reorder the terms: 2 + t = -2.645751311 Solving 2 + t = -2.645751311 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 = -2.645751311 + -2 Combine like terms: 2 + -2 = 0 0 + t = -2.645751311 + -2 t = -2.645751311 + -2 Combine like terms: -2.645751311 + -2 = -4.645751311 t = -4.645751311 Simplifying t = -4.645751311Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.645751311, -4.645751311}Solution
t = {0.645751311, -4.645751311}
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