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Simplifying 2.3t2 + -12.4t + -999926.7 = 0 Reorder the terms: -999926.7 + -12.4t + 2.3t2 = 0 Solving -999926.7 + -12.4t + 2.3t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 2.3 the coefficient of the squared term: Divide each side by '2.3'. -434750.7391 + -5.391304348t + t2 = 0 Move the constant term to the right: Add '434750.7391' to each side of the equation. -434750.7391 + -5.391304348t + 434750.7391 + t2 = 0 + 434750.7391 Reorder the terms: -434750.7391 + 434750.7391 + -5.391304348t + t2 = 0 + 434750.7391 Combine like terms: -434750.7391 + 434750.7391 = 0.0000 0.0000 + -5.391304348t + t2 = 0 + 434750.7391 -5.391304348t + t2 = 0 + 434750.7391 Combine like terms: 0 + 434750.7391 = 434750.7391 -5.391304348t + t2 = 434750.7391 The t term is -5.391304348t. Take half its coefficient (-2.695652174). Square it (7.266540643) and add it to both sides. Add '7.266540643' to each side of the equation. -5.391304348t + 7.266540643 + t2 = 434750.7391 + 7.266540643 Reorder the terms: 7.266540643 + -5.391304348t + t2 = 434750.7391 + 7.266540643 Combine like terms: 434750.7391 + 7.266540643 = 434758.005640643 7.266540643 + -5.391304348t + t2 = 434758.005640643 Factor a perfect square on the left side: (t + -2.695652174)(t + -2.695652174) = 434758.005640643 Calculate the square root of the right side: 659.361816942 Break this problem into two subproblems by setting (t + -2.695652174) equal to 659.361816942 and -659.361816942.Subproblem 1
t + -2.695652174 = 659.361816942 Simplifying t + -2.695652174 = 659.361816942 Reorder the terms: -2.695652174 + t = 659.361816942 Solving -2.695652174 + t = 659.361816942 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.695652174' to each side of the equation. -2.695652174 + 2.695652174 + t = 659.361816942 + 2.695652174 Combine like terms: -2.695652174 + 2.695652174 = 0.000000000 0.000000000 + t = 659.361816942 + 2.695652174 t = 659.361816942 + 2.695652174 Combine like terms: 659.361816942 + 2.695652174 = 662.057469116 t = 662.057469116 Simplifying t = 662.057469116Subproblem 2
t + -2.695652174 = -659.361816942 Simplifying t + -2.695652174 = -659.361816942 Reorder the terms: -2.695652174 + t = -659.361816942 Solving -2.695652174 + t = -659.361816942 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.695652174' to each side of the equation. -2.695652174 + 2.695652174 + t = -659.361816942 + 2.695652174 Combine like terms: -2.695652174 + 2.695652174 = 0.000000000 0.000000000 + t = -659.361816942 + 2.695652174 t = -659.361816942 + 2.695652174 Combine like terms: -659.361816942 + 2.695652174 = -656.666164768 t = -656.666164768 Simplifying t = -656.666164768Solution
The solution to the problem is based on the solutions from the subproblems. t = {662.057469116, -656.666164768}
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