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Simplifying 150 = 16t2 + 32t Reorder the terms: 150 = 32t + 16t2 Solving 150 = 32t + 16t2 Solving for variable 't'. Reorder the terms: 150 + -32t + -16t2 = 32t + -32t + 16t2 + -16t2 Combine like terms: 32t + -32t = 0 150 + -32t + -16t2 = 0 + 16t2 + -16t2 150 + -32t + -16t2 = 16t2 + -16t2 Combine like terms: 16t2 + -16t2 = 0 150 + -32t + -16t2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(75 + -16t + -8t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(75 + -16t + -8t2)' equal to zero and attempt to solve: Simplifying 75 + -16t + -8t2 = 0 Solving 75 + -16t + -8t2 = 0 Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. -9.375 + 2t + t2 = 0 Move the constant term to the right: Add '9.375' to each side of the equation. -9.375 + 2t + 9.375 + t2 = 0 + 9.375 Reorder the terms: -9.375 + 9.375 + 2t + t2 = 0 + 9.375 Combine like terms: -9.375 + 9.375 = 0.000 0.000 + 2t + t2 = 0 + 9.375 2t + t2 = 0 + 9.375 Combine like terms: 0 + 9.375 = 9.375 2t + t2 = 9.375 The t term is 2t. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2t + 1 + t2 = 9.375 + 1 Reorder the terms: 1 + 2t + t2 = 9.375 + 1 Combine like terms: 9.375 + 1 = 10.375 1 + 2t + t2 = 10.375 Factor a perfect square on the left side: (t + 1)(t + 1) = 10.375 Calculate the square root of the right side: 3.221024682 Break this problem into two subproblems by setting (t + 1) equal to 3.221024682 and -3.221024682.Subproblem 1
t + 1 = 3.221024682 Simplifying t + 1 = 3.221024682 Reorder the terms: 1 + t = 3.221024682 Solving 1 + t = 3.221024682 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + t = 3.221024682 + -1 Combine like terms: 1 + -1 = 0 0 + t = 3.221024682 + -1 t = 3.221024682 + -1 Combine like terms: 3.221024682 + -1 = 2.221024682 t = 2.221024682 Simplifying t = 2.221024682Subproblem 2
t + 1 = -3.221024682 Simplifying t + 1 = -3.221024682 Reorder the terms: 1 + t = -3.221024682 Solving 1 + t = -3.221024682 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + t = -3.221024682 + -1 Combine like terms: 1 + -1 = 0 0 + t = -3.221024682 + -1 t = -3.221024682 + -1 Combine like terms: -3.221024682 + -1 = -4.221024682 t = -4.221024682 Simplifying t = -4.221024682Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.221024682, -4.221024682}Solution
t = {2.221024682, -4.221024682}
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