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Simplifying -16t2 + 150t = 15 Reorder the terms: 150t + -16t2 = 15 Solving 150t + -16t2 = 15 Solving for variable 't'. Reorder the terms: -15 + 150t + -16t2 = 15 + -15 Combine like terms: 15 + -15 = 0 -15 + 150t + -16t2 = 0 Begin completing the square. Divide all terms by -16 the coefficient of the squared term: Divide each side by '-16'. 0.9375 + -9.375t + t2 = 0 Move the constant term to the right: Add '-0.9375' to each side of the equation. 0.9375 + -9.375t + -0.9375 + t2 = 0 + -0.9375 Reorder the terms: 0.9375 + -0.9375 + -9.375t + t2 = 0 + -0.9375 Combine like terms: 0.9375 + -0.9375 = 0.0000 0.0000 + -9.375t + t2 = 0 + -0.9375 -9.375t + t2 = 0 + -0.9375 Combine like terms: 0 + -0.9375 = -0.9375 -9.375t + t2 = -0.9375 The t term is -9.375t. Take half its coefficient (-4.6875). Square it (21.97265625) and add it to both sides. Add '21.97265625' to each side of the equation. -9.375t + 21.97265625 + t2 = -0.9375 + 21.97265625 Reorder the terms: 21.97265625 + -9.375t + t2 = -0.9375 + 21.97265625 Combine like terms: -0.9375 + 21.97265625 = 21.03515625 21.97265625 + -9.375t + t2 = 21.03515625 Factor a perfect square on the left side: (t + -4.6875)(t + -4.6875) = 21.03515625 Calculate the square root of the right side: 4.586409952 Break this problem into two subproblems by setting (t + -4.6875) equal to 4.586409952 and -4.586409952.Subproblem 1
t + -4.6875 = 4.586409952 Simplifying t + -4.6875 = 4.586409952 Reorder the terms: -4.6875 + t = 4.586409952 Solving -4.6875 + t = 4.586409952 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '4.6875' to each side of the equation. -4.6875 + 4.6875 + t = 4.586409952 + 4.6875 Combine like terms: -4.6875 + 4.6875 = 0.0000 0.0000 + t = 4.586409952 + 4.6875 t = 4.586409952 + 4.6875 Combine like terms: 4.586409952 + 4.6875 = 9.273909952 t = 9.273909952 Simplifying t = 9.273909952Subproblem 2
t + -4.6875 = -4.586409952 Simplifying t + -4.6875 = -4.586409952 Reorder the terms: -4.6875 + t = -4.586409952 Solving -4.6875 + t = -4.586409952 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '4.6875' to each side of the equation. -4.6875 + 4.6875 + t = -4.586409952 + 4.6875 Combine like terms: -4.6875 + 4.6875 = 0.0000 0.0000 + t = -4.586409952 + 4.6875 t = -4.586409952 + 4.6875 Combine like terms: -4.586409952 + 4.6875 = 0.101090048 t = 0.101090048 Simplifying t = 0.101090048Solution
The solution to the problem is based on the solutions from the subproblems. t = {9.273909952, 0.101090048}
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