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Simplifying 14 = 32t + 16t2 Solving 14 = 32t + 16t2 Solving for variable 't'. Reorder the terms: 14 + -32t + -16t2 = 32t + -32t + 16t2 + -16t2 Combine like terms: 32t + -32t = 0 14 + -32t + -16t2 = 0 + 16t2 + -16t2 14 + -32t + -16t2 = 16t2 + -16t2 Combine like terms: 16t2 + -16t2 = 0 14 + -32t + -16t2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(7 + -16t + -8t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(7 + -16t + -8t2)' equal to zero and attempt to solve: Simplifying 7 + -16t + -8t2 = 0 Solving 7 + -16t + -8t2 = 0 Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. -0.875 + 2t + t2 = 0 Move the constant term to the right: Add '0.875' to each side of the equation. -0.875 + 2t + 0.875 + t2 = 0 + 0.875 Reorder the terms: -0.875 + 0.875 + 2t + t2 = 0 + 0.875 Combine like terms: -0.875 + 0.875 = 0.000 0.000 + 2t + t2 = 0 + 0.875 2t + t2 = 0 + 0.875 Combine like terms: 0 + 0.875 = 0.875 2t + t2 = 0.875 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 = 0.875 + 1 Reorder the terms: 1 + 2t + t2 = 0.875 + 1 Combine like terms: 0.875 + 1 = 1.875 1 + 2t + t2 = 1.875 Factor a perfect square on the left side: (t + 1)(t + 1) = 1.875 Calculate the square root of the right side: 1.369306394 Break this problem into two subproblems by setting (t + 1) equal to 1.369306394 and -1.369306394.Subproblem 1
t + 1 = 1.369306394 Simplifying t + 1 = 1.369306394 Reorder the terms: 1 + t = 1.369306394 Solving 1 + t = 1.369306394 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 = 1.369306394 + -1 Combine like terms: 1 + -1 = 0 0 + t = 1.369306394 + -1 t = 1.369306394 + -1 Combine like terms: 1.369306394 + -1 = 0.369306394 t = 0.369306394 Simplifying t = 0.369306394Subproblem 2
t + 1 = -1.369306394 Simplifying t + 1 = -1.369306394 Reorder the terms: 1 + t = -1.369306394 Solving 1 + t = -1.369306394 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 = -1.369306394 + -1 Combine like terms: 1 + -1 = 0 0 + t = -1.369306394 + -1 t = -1.369306394 + -1 Combine like terms: -1.369306394 + -1 = -2.369306394 t = -2.369306394 Simplifying t = -2.369306394Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.369306394, -2.369306394}Solution
t = {0.369306394, -2.369306394}
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