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Simplifying 0 = -4.9t2 + 26t + 45 Reorder the terms: 0 = 45 + 26t + -4.9t2 Solving 0 = 45 + 26t + -4.9t2 Solving for variable 't'. Combine like terms: 0 + -45 = -45 -45 + -26t + 4.9t2 = 45 + 26t + -4.9t2 + -45 + -26t + 4.9t2 Reorder the terms: -45 + -26t + 4.9t2 = 45 + -45 + 26t + -26t + -4.9t2 + 4.9t2 Combine like terms: 45 + -45 = 0 -45 + -26t + 4.9t2 = 0 + 26t + -26t + -4.9t2 + 4.9t2 -45 + -26t + 4.9t2 = 26t + -26t + -4.9t2 + 4.9t2 Combine like terms: 26t + -26t = 0 -45 + -26t + 4.9t2 = 0 + -4.9t2 + 4.9t2 -45 + -26t + 4.9t2 = -4.9t2 + 4.9t2 Combine like terms: -4.9t2 + 4.9t2 = 0.0 -45 + -26t + 4.9t2 = 0.0 Begin completing the square. Divide all terms by 4.9 the coefficient of the squared term: Divide each side by '4.9'. -9.183673469 + -5.306122449t + t2 = 0 Move the constant term to the right: Add '9.183673469' to each side of the equation. -9.183673469 + -5.306122449t + 9.183673469 + t2 = 0 + 9.183673469 Reorder the terms: -9.183673469 + 9.183673469 + -5.306122449t + t2 = 0 + 9.183673469 Combine like terms: -9.183673469 + 9.183673469 = 0.000000000 0.000000000 + -5.306122449t + t2 = 0 + 9.183673469 -5.306122449t + t2 = 0 + 9.183673469 Combine like terms: 0 + 9.183673469 = 9.183673469 -5.306122449t + t2 = 9.183673469 The t term is -5.306122449t. Take half its coefficient (-2.653061225). Square it (7.038733864) and add it to both sides. Add '7.038733864' to each side of the equation. -5.306122449t + 7.038733864 + t2 = 9.183673469 + 7.038733864 Reorder the terms: 7.038733864 + -5.306122449t + t2 = 9.183673469 + 7.038733864 Combine like terms: 9.183673469 + 7.038733864 = 16.222407333 7.038733864 + -5.306122449t + t2 = 16.222407333 Factor a perfect square on the left side: (t + -2.653061225)(t + -2.653061225) = 16.222407333 Calculate the square root of the right side: 4.027704971 Break this problem into two subproblems by setting (t + -2.653061225) equal to 4.027704971 and -4.027704971.Subproblem 1
t + -2.653061225 = 4.027704971 Simplifying t + -2.653061225 = 4.027704971 Reorder the terms: -2.653061225 + t = 4.027704971 Solving -2.653061225 + t = 4.027704971 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.653061225' to each side of the equation. -2.653061225 + 2.653061225 + t = 4.027704971 + 2.653061225 Combine like terms: -2.653061225 + 2.653061225 = 0.000000000 0.000000000 + t = 4.027704971 + 2.653061225 t = 4.027704971 + 2.653061225 Combine like terms: 4.027704971 + 2.653061225 = 6.680766196 t = 6.680766196 Simplifying t = 6.680766196Subproblem 2
t + -2.653061225 = -4.027704971 Simplifying t + -2.653061225 = -4.027704971 Reorder the terms: -2.653061225 + t = -4.027704971 Solving -2.653061225 + t = -4.027704971 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.653061225' to each side of the equation. -2.653061225 + 2.653061225 + t = -4.027704971 + 2.653061225 Combine like terms: -2.653061225 + 2.653061225 = 0.000000000 0.000000000 + t = -4.027704971 + 2.653061225 t = -4.027704971 + 2.653061225 Combine like terms: -4.027704971 + 2.653061225 = -1.374643746 t = -1.374643746 Simplifying t = -1.374643746Solution
The solution to the problem is based on the solutions from the subproblems. t = {6.680766196, -1.374643746}
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