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Simplifying -20.3 = 11.5t + 0.5(-9.8) * t2 Multiply 0.5 * -9.8 -20.3 = 11.5t + -4.9t2 Solving -20.3 = 11.5t + -4.9t2 Solving for variable 't'. Reorder the terms: -20.3 + -11.5t + 4.9t2 = 11.5t + -11.5t + -4.9t2 + 4.9t2 Combine like terms: 11.5t + -11.5t = 0.0 -20.3 + -11.5t + 4.9t2 = 0.0 + -4.9t2 + 4.9t2 -20.3 + -11.5t + 4.9t2 = -4.9t2 + 4.9t2 Combine like terms: -4.9t2 + 4.9t2 = 0.0 -20.3 + -11.5t + 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'. -4.142857143 + -2.346938776t + t2 = 0 Move the constant term to the right: Add '4.142857143' to each side of the equation. -4.142857143 + -2.346938776t + 4.142857143 + t2 = 0 + 4.142857143 Reorder the terms: -4.142857143 + 4.142857143 + -2.346938776t + t2 = 0 + 4.142857143 Combine like terms: -4.142857143 + 4.142857143 = 0.000000000 0.000000000 + -2.346938776t + t2 = 0 + 4.142857143 -2.346938776t + t2 = 0 + 4.142857143 Combine like terms: 0 + 4.142857143 = 4.142857143 -2.346938776t + t2 = 4.142857143 The t term is -2.346938776t. Take half its coefficient (-1.173469388). Square it (1.377030405) and add it to both sides. Add '1.377030405' to each side of the equation. -2.346938776t + 1.377030405 + t2 = 4.142857143 + 1.377030405 Reorder the terms: 1.377030405 + -2.346938776t + t2 = 4.142857143 + 1.377030405 Combine like terms: 4.142857143 + 1.377030405 = 5.519887548 1.377030405 + -2.346938776t + t2 = 5.519887548 Factor a perfect square on the left side: (t + -1.173469388)(t + -1.173469388) = 5.519887548 Calculate the square root of the right side: 2.349444093 Break this problem into two subproblems by setting (t + -1.173469388) equal to 2.349444093 and -2.349444093.Subproblem 1
t + -1.173469388 = 2.349444093 Simplifying t + -1.173469388 = 2.349444093 Reorder the terms: -1.173469388 + t = 2.349444093 Solving -1.173469388 + t = 2.349444093 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.173469388' to each side of the equation. -1.173469388 + 1.173469388 + t = 2.349444093 + 1.173469388 Combine like terms: -1.173469388 + 1.173469388 = 0.000000000 0.000000000 + t = 2.349444093 + 1.173469388 t = 2.349444093 + 1.173469388 Combine like terms: 2.349444093 + 1.173469388 = 3.522913481 t = 3.522913481 Simplifying t = 3.522913481Subproblem 2
t + -1.173469388 = -2.349444093 Simplifying t + -1.173469388 = -2.349444093 Reorder the terms: -1.173469388 + t = -2.349444093 Solving -1.173469388 + t = -2.349444093 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.173469388' to each side of the equation. -1.173469388 + 1.173469388 + t = -2.349444093 + 1.173469388 Combine like terms: -1.173469388 + 1.173469388 = 0.000000000 0.000000000 + t = -2.349444093 + 1.173469388 t = -2.349444093 + 1.173469388 Combine like terms: -2.349444093 + 1.173469388 = -1.175974705 t = -1.175974705 Simplifying t = -1.175974705Solution
The solution to the problem is based on the solutions from the subproblems. t = {3.522913481, -1.175974705}
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