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Simplifying 70 = -4.9t2 + 19.6t + 58.8 Reorder the terms: 70 = 58.8 + 19.6t + -4.9t2 Solving 70 = 58.8 + 19.6t + -4.9t2 Solving for variable 't'. Combine like terms: 70 + -58.8 = 11.2 11.2 + -19.6t + 4.9t2 = 58.8 + 19.6t + -4.9t2 + -58.8 + -19.6t + 4.9t2 Reorder the terms: 11.2 + -19.6t + 4.9t2 = 58.8 + -58.8 + 19.6t + -19.6t + -4.9t2 + 4.9t2 Combine like terms: 58.8 + -58.8 = 0.0 11.2 + -19.6t + 4.9t2 = 0.0 + 19.6t + -19.6t + -4.9t2 + 4.9t2 11.2 + -19.6t + 4.9t2 = 19.6t + -19.6t + -4.9t2 + 4.9t2 Combine like terms: 19.6t + -19.6t = 0.0 11.2 + -19.6t + 4.9t2 = 0.0 + -4.9t2 + 4.9t2 11.2 + -19.6t + 4.9t2 = -4.9t2 + 4.9t2 Combine like terms: -4.9t2 + 4.9t2 = 0.0 11.2 + -19.6t + 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'. 2.285714286 + -4t + t2 = 0 Move the constant term to the right: Add '-2.285714286' to each side of the equation. 2.285714286 + -4t + -2.285714286 + t2 = 0 + -2.285714286 Reorder the terms: 2.285714286 + -2.285714286 + -4t + t2 = 0 + -2.285714286 Combine like terms: 2.285714286 + -2.285714286 = 0.000000000 0.000000000 + -4t + t2 = 0 + -2.285714286 -4t + t2 = 0 + -2.285714286 Combine like terms: 0 + -2.285714286 = -2.285714286 -4t + t2 = -2.285714286 The t term is -4t. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4t + 4 + t2 = -2.285714286 + 4 Reorder the terms: 4 + -4t + t2 = -2.285714286 + 4 Combine like terms: -2.285714286 + 4 = 1.714285714 4 + -4t + t2 = 1.714285714 Factor a perfect square on the left side: (t + -2)(t + -2) = 1.714285714 Calculate the square root of the right side: 1.309307341 Break this problem into two subproblems by setting (t + -2) equal to 1.309307341 and -1.309307341.Subproblem 1
t + -2 = 1.309307341 Simplifying t + -2 = 1.309307341 Reorder the terms: -2 + t = 1.309307341 Solving -2 + t = 1.309307341 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + t = 1.309307341 + 2 Combine like terms: -2 + 2 = 0 0 + t = 1.309307341 + 2 t = 1.309307341 + 2 Combine like terms: 1.309307341 + 2 = 3.309307341 t = 3.309307341 Simplifying t = 3.309307341Subproblem 2
t + -2 = -1.309307341 Simplifying t + -2 = -1.309307341 Reorder the terms: -2 + t = -1.309307341 Solving -2 + t = -1.309307341 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + t = -1.309307341 + 2 Combine like terms: -2 + 2 = 0 0 + t = -1.309307341 + 2 t = -1.309307341 + 2 Combine like terms: -1.309307341 + 2 = 0.690692659 t = 0.690692659 Simplifying t = 0.690692659Solution
The solution to the problem is based on the solutions from the subproblems. t = {3.309307341, 0.690692659}
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