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Simplifying 0 = -4.9t2 + 42t + 10 Reorder the terms: 0 = 10 + 42t + -4.9t2 Solving 0 = 10 + 42t + -4.9t2 Solving for variable 't'. Combine like terms: 0 + -10 = -10 -10 + -42t + 4.9t2 = 10 + 42t + -4.9t2 + -10 + -42t + 4.9t2 Reorder the terms: -10 + -42t + 4.9t2 = 10 + -10 + 42t + -42t + -4.9t2 + 4.9t2 Combine like terms: 10 + -10 = 0 -10 + -42t + 4.9t2 = 0 + 42t + -42t + -4.9t2 + 4.9t2 -10 + -42t + 4.9t2 = 42t + -42t + -4.9t2 + 4.9t2 Combine like terms: 42t + -42t = 0 -10 + -42t + 4.9t2 = 0 + -4.9t2 + 4.9t2 -10 + -42t + 4.9t2 = -4.9t2 + 4.9t2 Combine like terms: -4.9t2 + 4.9t2 = 0.0 -10 + -42t + 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'. -2.040816327 + -8.571428571t + t2 = 0 Move the constant term to the right: Add '2.040816327' to each side of the equation. -2.040816327 + -8.571428571t + 2.040816327 + t2 = 0 + 2.040816327 Reorder the terms: -2.040816327 + 2.040816327 + -8.571428571t + t2 = 0 + 2.040816327 Combine like terms: -2.040816327 + 2.040816327 = 0.000000000 0.000000000 + -8.571428571t + t2 = 0 + 2.040816327 -8.571428571t + t2 = 0 + 2.040816327 Combine like terms: 0 + 2.040816327 = 2.040816327 -8.571428571t + t2 = 2.040816327 The t term is -8.571428571t. Take half its coefficient (-4.285714286). Square it (18.36734694) and add it to both sides. Add '18.36734694' to each side of the equation. -8.571428571t + 18.36734694 + t2 = 2.040816327 + 18.36734694 Reorder the terms: 18.36734694 + -8.571428571t + t2 = 2.040816327 + 18.36734694 Combine like terms: 2.040816327 + 18.36734694 = 20.408163267 18.36734694 + -8.571428571t + t2 = 20.408163267 Factor a perfect square on the left side: (t + -4.285714286)(t + -4.285714286) = 20.408163267 Calculate the square root of the right side: 4.517539515 Break this problem into two subproblems by setting (t + -4.285714286) equal to 4.517539515 and -4.517539515.Subproblem 1
t + -4.285714286 = 4.517539515 Simplifying t + -4.285714286 = 4.517539515 Reorder the terms: -4.285714286 + t = 4.517539515 Solving -4.285714286 + t = 4.517539515 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '4.285714286' to each side of the equation. -4.285714286 + 4.285714286 + t = 4.517539515 + 4.285714286 Combine like terms: -4.285714286 + 4.285714286 = 0.000000000 0.000000000 + t = 4.517539515 + 4.285714286 t = 4.517539515 + 4.285714286 Combine like terms: 4.517539515 + 4.285714286 = 8.803253801 t = 8.803253801 Simplifying t = 8.803253801Subproblem 2
t + -4.285714286 = -4.517539515 Simplifying t + -4.285714286 = -4.517539515 Reorder the terms: -4.285714286 + t = -4.517539515 Solving -4.285714286 + t = -4.517539515 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '4.285714286' to each side of the equation. -4.285714286 + 4.285714286 + t = -4.517539515 + 4.285714286 Combine like terms: -4.285714286 + 4.285714286 = 0.000000000 0.000000000 + t = -4.517539515 + 4.285714286 t = -4.517539515 + 4.285714286 Combine like terms: -4.517539515 + 4.285714286 = -0.231825229 t = -0.231825229 Simplifying t = -0.231825229Solution
The solution to the problem is based on the solutions from the subproblems. t = {8.803253801, -0.231825229}
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