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Simplifying 4.9t2 + -21.3t + 15 = 0 Reorder the terms: 15 + -21.3t + 4.9t2 = 0 Solving 15 + -21.3t + 4.9t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 4.9 the coefficient of the squared term: Divide each side by '4.9'. 3.06122449 + -4.346938776t + t2 = 0 Move the constant term to the right: Add '-3.06122449' to each side of the equation. 3.06122449 + -4.346938776t + -3.06122449 + t2 = 0 + -3.06122449 Reorder the terms: 3.06122449 + -3.06122449 + -4.346938776t + t2 = 0 + -3.06122449 Combine like terms: 3.06122449 + -3.06122449 = 0.00000000 0.00000000 + -4.346938776t + t2 = 0 + -3.06122449 -4.346938776t + t2 = 0 + -3.06122449 Combine like terms: 0 + -3.06122449 = -3.06122449 -4.346938776t + t2 = -3.06122449 The t term is -4.346938776t. Take half its coefficient (-2.173469388). Square it (4.723969181) and add it to both sides. Add '4.723969181' to each side of the equation. -4.346938776t + 4.723969181 + t2 = -3.06122449 + 4.723969181 Reorder the terms: 4.723969181 + -4.346938776t + t2 = -3.06122449 + 4.723969181 Combine like terms: -3.06122449 + 4.723969181 = 1.662744691 4.723969181 + -4.346938776t + t2 = 1.662744691 Factor a perfect square on the left side: (t + -2.173469388)(t + -2.173469388) = 1.662744691 Calculate the square root of the right side: 1.289474579 Break this problem into two subproblems by setting (t + -2.173469388) equal to 1.289474579 and -1.289474579.Subproblem 1
t + -2.173469388 = 1.289474579 Simplifying t + -2.173469388 = 1.289474579 Reorder the terms: -2.173469388 + t = 1.289474579 Solving -2.173469388 + t = 1.289474579 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.173469388' to each side of the equation. -2.173469388 + 2.173469388 + t = 1.289474579 + 2.173469388 Combine like terms: -2.173469388 + 2.173469388 = 0.000000000 0.000000000 + t = 1.289474579 + 2.173469388 t = 1.289474579 + 2.173469388 Combine like terms: 1.289474579 + 2.173469388 = 3.462943967 t = 3.462943967 Simplifying t = 3.462943967Subproblem 2
t + -2.173469388 = -1.289474579 Simplifying t + -2.173469388 = -1.289474579 Reorder the terms: -2.173469388 + t = -1.289474579 Solving -2.173469388 + t = -1.289474579 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.173469388' to each side of the equation. -2.173469388 + 2.173469388 + t = -1.289474579 + 2.173469388 Combine like terms: -2.173469388 + 2.173469388 = 0.000000000 0.000000000 + t = -1.289474579 + 2.173469388 t = -1.289474579 + 2.173469388 Combine like terms: -1.289474579 + 2.173469388 = 0.883994809 t = 0.883994809 Simplifying t = 0.883994809Solution
The solution to the problem is based on the solutions from the subproblems. t = {3.462943967, 0.883994809}
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