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Simplifying 150 = 16t2 + -130t Reorder the terms: 150 = -130t + 16t2 Solving 150 = -130t + 16t2 Solving for variable 't'. Reorder the terms: 150 + 130t + -16t2 = -130t + 130t + 16t2 + -16t2 Combine like terms: -130t + 130t = 0 150 + 130t + -16t2 = 0 + 16t2 + -16t2 150 + 130t + -16t2 = 16t2 + -16t2 Combine like terms: 16t2 + -16t2 = 0 150 + 130t + -16t2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(75 + 65t + -8t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(75 + 65t + -8t2)' equal to zero and attempt to solve: Simplifying 75 + 65t + -8t2 = 0 Solving 75 + 65t + -8t2 = 0 Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. -9.375 + -8.125t + t2 = 0 Move the constant term to the right: Add '9.375' to each side of the equation. -9.375 + -8.125t + 9.375 + t2 = 0 + 9.375 Reorder the terms: -9.375 + 9.375 + -8.125t + t2 = 0 + 9.375 Combine like terms: -9.375 + 9.375 = 0.000 0.000 + -8.125t + t2 = 0 + 9.375 -8.125t + t2 = 0 + 9.375 Combine like terms: 0 + 9.375 = 9.375 -8.125t + t2 = 9.375 The t term is -8.125t. Take half its coefficient (-4.0625). Square it (16.50390625) and add it to both sides. Add '16.50390625' to each side of the equation. -8.125t + 16.50390625 + t2 = 9.375 + 16.50390625 Reorder the terms: 16.50390625 + -8.125t + t2 = 9.375 + 16.50390625 Combine like terms: 9.375 + 16.50390625 = 25.87890625 16.50390625 + -8.125t + t2 = 25.87890625 Factor a perfect square on the left side: (t + -4.0625)(t + -4.0625) = 25.87890625 Calculate the square root of the right side: 5.087131436 Break this problem into two subproblems by setting (t + -4.0625) equal to 5.087131436 and -5.087131436.Subproblem 1
t + -4.0625 = 5.087131436 Simplifying t + -4.0625 = 5.087131436 Reorder the terms: -4.0625 + t = 5.087131436 Solving -4.0625 + t = 5.087131436 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '4.0625' to each side of the equation. -4.0625 + 4.0625 + t = 5.087131436 + 4.0625 Combine like terms: -4.0625 + 4.0625 = 0.0000 0.0000 + t = 5.087131436 + 4.0625 t = 5.087131436 + 4.0625 Combine like terms: 5.087131436 + 4.0625 = 9.149631436 t = 9.149631436 Simplifying t = 9.149631436Subproblem 2
t + -4.0625 = -5.087131436 Simplifying t + -4.0625 = -5.087131436 Reorder the terms: -4.0625 + t = -5.087131436 Solving -4.0625 + t = -5.087131436 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '4.0625' to each side of the equation. -4.0625 + 4.0625 + t = -5.087131436 + 4.0625 Combine like terms: -4.0625 + 4.0625 = 0.0000 0.0000 + t = -5.087131436 + 4.0625 t = -5.087131436 + 4.0625 Combine like terms: -5.087131436 + 4.0625 = -1.024631436 t = -1.024631436 Simplifying t = -1.024631436Solution
The solution to the problem is based on the solutions from the subproblems. t = {9.149631436, -1.024631436}Solution
t = {9.149631436, -1.024631436}
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