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Simplifying 1.95t2 + -35.5t + -248.5 = 0 Reorder the terms: -248.5 + -35.5t + 1.95t2 = 0 Solving -248.5 + -35.5t + 1.95t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 1.95 the coefficient of the squared term: Divide each side by '1.95'. -127.4358974 + -18.20512821t + t2 = 0 Move the constant term to the right: Add '127.4358974' to each side of the equation. -127.4358974 + -18.20512821t + 127.4358974 + t2 = 0 + 127.4358974 Reorder the terms: -127.4358974 + 127.4358974 + -18.20512821t + t2 = 0 + 127.4358974 Combine like terms: -127.4358974 + 127.4358974 = 0.0000000 0.0000000 + -18.20512821t + t2 = 0 + 127.4358974 -18.20512821t + t2 = 0 + 127.4358974 Combine like terms: 0 + 127.4358974 = 127.4358974 -18.20512821t + t2 = 127.4358974 The t term is -18.20512821t. Take half its coefficient (-9.102564105). Square it (82.85667329) and add it to both sides. Add '82.85667329' to each side of the equation. -18.20512821t + 82.85667329 + t2 = 127.4358974 + 82.85667329 Reorder the terms: 82.85667329 + -18.20512821t + t2 = 127.4358974 + 82.85667329 Combine like terms: 127.4358974 + 82.85667329 = 210.29257069 82.85667329 + -18.20512821t + t2 = 210.29257069 Factor a perfect square on the left side: (t + -9.102564105)(t + -9.102564105) = 210.29257069 Calculate the square root of the right side: 14.501467881 Break this problem into two subproblems by setting (t + -9.102564105) equal to 14.501467881 and -14.501467881.Subproblem 1
t + -9.102564105 = 14.501467881 Simplifying t + -9.102564105 = 14.501467881 Reorder the terms: -9.102564105 + t = 14.501467881 Solving -9.102564105 + t = 14.501467881 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '9.102564105' to each side of the equation. -9.102564105 + 9.102564105 + t = 14.501467881 + 9.102564105 Combine like terms: -9.102564105 + 9.102564105 = 0.000000000 0.000000000 + t = 14.501467881 + 9.102564105 t = 14.501467881 + 9.102564105 Combine like terms: 14.501467881 + 9.102564105 = 23.604031986 t = 23.604031986 Simplifying t = 23.604031986Subproblem 2
t + -9.102564105 = -14.501467881 Simplifying t + -9.102564105 = -14.501467881 Reorder the terms: -9.102564105 + t = -14.501467881 Solving -9.102564105 + t = -14.501467881 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '9.102564105' to each side of the equation. -9.102564105 + 9.102564105 + t = -14.501467881 + 9.102564105 Combine like terms: -9.102564105 + 9.102564105 = 0.000000000 0.000000000 + t = -14.501467881 + 9.102564105 t = -14.501467881 + 9.102564105 Combine like terms: -14.501467881 + 9.102564105 = -5.398903776 t = -5.398903776 Simplifying t = -5.398903776Solution
The solution to the problem is based on the solutions from the subproblems. t = {23.604031986, -5.398903776}
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