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Simplifying 20 = 13.3t + 4.9t2 Solving 20 = 13.3t + 4.9t2 Solving for variable 't'. Reorder the terms: 20 + -13.3t + -4.9t2 = 13.3t + -13.3t + 4.9t2 + -4.9t2 Combine like terms: 13.3t + -13.3t = 0.0 20 + -13.3t + -4.9t2 = 0.0 + 4.9t2 + -4.9t2 20 + -13.3t + -4.9t2 = 4.9t2 + -4.9t2 Combine like terms: 4.9t2 + -4.9t2 = 0.0 20 + -13.3t + -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'. -4.081632653 + 2.714285714t + t2 = 0 Move the constant term to the right: Add '4.081632653' to each side of the equation. -4.081632653 + 2.714285714t + 4.081632653 + t2 = 0 + 4.081632653 Reorder the terms: -4.081632653 + 4.081632653 + 2.714285714t + t2 = 0 + 4.081632653 Combine like terms: -4.081632653 + 4.081632653 = 0.000000000 0.000000000 + 2.714285714t + t2 = 0 + 4.081632653 2.714285714t + t2 = 0 + 4.081632653 Combine like terms: 0 + 4.081632653 = 4.081632653 2.714285714t + t2 = 4.081632653 The t term is 2.714285714t. Take half its coefficient (1.357142857). Square it (1.841836734) and add it to both sides. Add '1.841836734' to each side of the equation. 2.714285714t + 1.841836734 + t2 = 4.081632653 + 1.841836734 Reorder the terms: 1.841836734 + 2.714285714t + t2 = 4.081632653 + 1.841836734 Combine like terms: 4.081632653 + 1.841836734 = 5.923469387 1.841836734 + 2.714285714t + t2 = 5.923469387 Factor a perfect square on the left side: (t + 1.357142857)(t + 1.357142857) = 5.923469387 Calculate the square root of the right side: 2.433817862 Break this problem into two subproblems by setting (t + 1.357142857) equal to 2.433817862 and -2.433817862.Subproblem 1
t + 1.357142857 = 2.433817862 Simplifying t + 1.357142857 = 2.433817862 Reorder the terms: 1.357142857 + t = 2.433817862 Solving 1.357142857 + t = 2.433817862 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-1.357142857' to each side of the equation. 1.357142857 + -1.357142857 + t = 2.433817862 + -1.357142857 Combine like terms: 1.357142857 + -1.357142857 = 0.000000000 0.000000000 + t = 2.433817862 + -1.357142857 t = 2.433817862 + -1.357142857 Combine like terms: 2.433817862 + -1.357142857 = 1.076675005 t = 1.076675005 Simplifying t = 1.076675005Subproblem 2
t + 1.357142857 = -2.433817862 Simplifying t + 1.357142857 = -2.433817862 Reorder the terms: 1.357142857 + t = -2.433817862 Solving 1.357142857 + t = -2.433817862 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-1.357142857' to each side of the equation. 1.357142857 + -1.357142857 + t = -2.433817862 + -1.357142857 Combine like terms: 1.357142857 + -1.357142857 = 0.000000000 0.000000000 + t = -2.433817862 + -1.357142857 t = -2.433817862 + -1.357142857 Combine like terms: -2.433817862 + -1.357142857 = -3.790960719 t = -3.790960719 Simplifying t = -3.790960719Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.076675005, -3.790960719}
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