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Simplifying t = -16t2 + 18 Reorder the terms: t = 18 + -16t2 Solving t = 18 + -16t2 Solving for variable 't'. Reorder the terms: -18 + t + 16t2 = 18 + -16t2 + -18 + 16t2 Reorder the terms: -18 + t + 16t2 = 18 + -18 + -16t2 + 16t2 Combine like terms: 18 + -18 = 0 -18 + t + 16t2 = 0 + -16t2 + 16t2 -18 + t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -18 + t + 16t2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -1.125 + 0.0625t + t2 = 0 Move the constant term to the right: Add '1.125' to each side of the equation. -1.125 + 0.0625t + 1.125 + t2 = 0 + 1.125 Reorder the terms: -1.125 + 1.125 + 0.0625t + t2 = 0 + 1.125 Combine like terms: -1.125 + 1.125 = 0.000 0.000 + 0.0625t + t2 = 0 + 1.125 0.0625t + t2 = 0 + 1.125 Combine like terms: 0 + 1.125 = 1.125 0.0625t + t2 = 1.125 The t term is t. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. 0.0625t + 0.25 + t2 = 1.125 + 0.25 Reorder the terms: 0.25 + 0.0625t + t2 = 1.125 + 0.25 Combine like terms: 1.125 + 0.25 = 1.375 0.25 + 0.0625t + t2 = 1.375 Factor a perfect square on the left side: (t + 0.5)(t + 0.5) = 1.375 Calculate the square root of the right side: 1.17260394 Break this problem into two subproblems by setting (t + 0.5) equal to 1.17260394 and -1.17260394.Subproblem 1
t + 0.5 = 1.17260394 Simplifying t + 0.5 = 1.17260394 Reorder the terms: 0.5 + t = 1.17260394 Solving 0.5 + t = 1.17260394 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + t = 1.17260394 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + t = 1.17260394 + -0.5 t = 1.17260394 + -0.5 Combine like terms: 1.17260394 + -0.5 = 0.67260394 t = 0.67260394 Simplifying t = 0.67260394Subproblem 2
t + 0.5 = -1.17260394 Simplifying t + 0.5 = -1.17260394 Reorder the terms: 0.5 + t = -1.17260394 Solving 0.5 + t = -1.17260394 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + t = -1.17260394 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + t = -1.17260394 + -0.5 t = -1.17260394 + -0.5 Combine like terms: -1.17260394 + -0.5 = -1.67260394 t = -1.67260394 Simplifying t = -1.67260394Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.67260394, -1.67260394}
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