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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 = 3.790960719 t = 3.790960719 Simplifying t = 3.790960719Subproblem 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 = -1.076675005 t = -1.076675005 Simplifying t = -1.076675005Solution
The solution to the problem is based on the solutions from the subproblems. t = {3.790960719, -1.076675005}
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