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Simplifying 180 = -4.9t2 + 67t Reorder the terms: 180 = 67t + -4.9t2 Solving 180 = 67t + -4.9t2 Solving for variable 't'. Reorder the terms: 180 + -67t + 4.9t2 = 67t + -67t + -4.9t2 + 4.9t2 Combine like terms: 67t + -67t = 0 180 + -67t + 4.9t2 = 0 + -4.9t2 + 4.9t2 180 + -67t + 4.9t2 = -4.9t2 + 4.9t2 Combine like terms: -4.9t2 + 4.9t2 = 0.0 180 + -67t + 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'. 36.73469388 + -13.67346939t + t2 = 0 Move the constant term to the right: Add '-36.73469388' to each side of the equation. 36.73469388 + -13.67346939t + -36.73469388 + t2 = 0 + -36.73469388 Reorder the terms: 36.73469388 + -36.73469388 + -13.67346939t + t2 = 0 + -36.73469388 Combine like terms: 36.73469388 + -36.73469388 = 0.00000000 0.00000000 + -13.67346939t + t2 = 0 + -36.73469388 -13.67346939t + t2 = 0 + -36.73469388 Combine like terms: 0 + -36.73469388 = -36.73469388 -13.67346939t + t2 = -36.73469388 The t term is -13.67346939t. Take half its coefficient (-6.836734695). Square it (46.74094129) and add it to both sides. Add '46.74094129' to each side of the equation. -13.67346939t + 46.74094129 + t2 = -36.73469388 + 46.74094129 Reorder the terms: 46.74094129 + -13.67346939t + t2 = -36.73469388 + 46.74094129 Combine like terms: -36.73469388 + 46.74094129 = 10.00624741 46.74094129 + -13.67346939t + t2 = 10.00624741 Factor a perfect square on the left side: (t + -6.836734695)(t + -6.836734695) = 10.00624741 Calculate the square root of the right side: 3.163265308 Break this problem into two subproblems by setting (t + -6.836734695) equal to 3.163265308 and -3.163265308.Subproblem 1
t + -6.836734695 = 3.163265308 Simplifying t + -6.836734695 = 3.163265308 Reorder the terms: -6.836734695 + t = 3.163265308 Solving -6.836734695 + t = 3.163265308 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '6.836734695' to each side of the equation. -6.836734695 + 6.836734695 + t = 3.163265308 + 6.836734695 Combine like terms: -6.836734695 + 6.836734695 = 0.000000000 0.000000000 + t = 3.163265308 + 6.836734695 t = 3.163265308 + 6.836734695 Combine like terms: 3.163265308 + 6.836734695 = 10.000000003 t = 10.000000003 Simplifying t = 10.000000003Subproblem 2
t + -6.836734695 = -3.163265308 Simplifying t + -6.836734695 = -3.163265308 Reorder the terms: -6.836734695 + t = -3.163265308 Solving -6.836734695 + t = -3.163265308 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '6.836734695' to each side of the equation. -6.836734695 + 6.836734695 + t = -3.163265308 + 6.836734695 Combine like terms: -6.836734695 + 6.836734695 = 0.000000000 0.000000000 + t = -3.163265308 + 6.836734695 t = -3.163265308 + 6.836734695 Combine like terms: -3.163265308 + 6.836734695 = 3.673469387 t = 3.673469387 Simplifying t = 3.673469387Solution
The solution to the problem is based on the solutions from the subproblems. t = {10.000000003, 3.673469387}
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