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Simplifying -150 = -16t2 + 7t + 4 Reorder the terms: -150 = 4 + 7t + -16t2 Solving -150 = 4 + 7t + -16t2 Solving for variable 't'. Combine like terms: -150 + -4 = -154 -154 + -7t + 16t2 = 4 + 7t + -16t2 + -4 + -7t + 16t2 Reorder the terms: -154 + -7t + 16t2 = 4 + -4 + 7t + -7t + -16t2 + 16t2 Combine like terms: 4 + -4 = 0 -154 + -7t + 16t2 = 0 + 7t + -7t + -16t2 + 16t2 -154 + -7t + 16t2 = 7t + -7t + -16t2 + 16t2 Combine like terms: 7t + -7t = 0 -154 + -7t + 16t2 = 0 + -16t2 + 16t2 -154 + -7t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -154 + -7t + 16t2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -9.625 + -0.4375t + t2 = 0 Move the constant term to the right: Add '9.625' to each side of the equation. -9.625 + -0.4375t + 9.625 + t2 = 0 + 9.625 Reorder the terms: -9.625 + 9.625 + -0.4375t + t2 = 0 + 9.625 Combine like terms: -9.625 + 9.625 = 0.000 0.000 + -0.4375t + t2 = 0 + 9.625 -0.4375t + t2 = 0 + 9.625 Combine like terms: 0 + 9.625 = 9.625 -0.4375t + t2 = 9.625 The t term is -0.4375t. Take half its coefficient (-0.21875). Square it (0.0478515625) and add it to both sides. Add '0.0478515625' to each side of the equation. -0.4375t + 0.0478515625 + t2 = 9.625 + 0.0478515625 Reorder the terms: 0.0478515625 + -0.4375t + t2 = 9.625 + 0.0478515625 Combine like terms: 9.625 + 0.0478515625 = 9.6728515625 0.0478515625 + -0.4375t + t2 = 9.6728515625 Factor a perfect square on the left side: (t + -0.21875)(t + -0.21875) = 9.6728515625 Calculate the square root of the right side: 3.110120828 Break this problem into two subproblems by setting (t + -0.21875) equal to 3.110120828 and -3.110120828.Subproblem 1
t + -0.21875 = 3.110120828 Simplifying t + -0.21875 = 3.110120828 Reorder the terms: -0.21875 + t = 3.110120828 Solving -0.21875 + t = 3.110120828 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.21875' to each side of the equation. -0.21875 + 0.21875 + t = 3.110120828 + 0.21875 Combine like terms: -0.21875 + 0.21875 = 0.00000 0.00000 + t = 3.110120828 + 0.21875 t = 3.110120828 + 0.21875 Combine like terms: 3.110120828 + 0.21875 = 3.328870828 t = 3.328870828 Simplifying t = 3.328870828Subproblem 2
t + -0.21875 = -3.110120828 Simplifying t + -0.21875 = -3.110120828 Reorder the terms: -0.21875 + t = -3.110120828 Solving -0.21875 + t = -3.110120828 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.21875' to each side of the equation. -0.21875 + 0.21875 + t = -3.110120828 + 0.21875 Combine like terms: -0.21875 + 0.21875 = 0.00000 0.00000 + t = -3.110120828 + 0.21875 t = -3.110120828 + 0.21875 Combine like terms: -3.110120828 + 0.21875 = -2.891370828 t = -2.891370828 Simplifying t = -2.891370828Solution
The solution to the problem is based on the solutions from the subproblems. t = {3.328870828, -2.891370828}
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