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Simplifying -16t2 + 7.85t + 57 = 0 Reorder the terms: 57 + 7.85t + -16t2 = 0 Solving 57 + 7.85t + -16t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by -16 the coefficient of the squared term: Divide each side by '-16'. -3.5625 + -0.490625t + t2 = 0 Move the constant term to the right: Add '3.5625' to each side of the equation. -3.5625 + -0.490625t + 3.5625 + t2 = 0 + 3.5625 Reorder the terms: -3.5625 + 3.5625 + -0.490625t + t2 = 0 + 3.5625 Combine like terms: -3.5625 + 3.5625 = 0.0000 0.0000 + -0.490625t + t2 = 0 + 3.5625 -0.490625t + t2 = 0 + 3.5625 Combine like terms: 0 + 3.5625 = 3.5625 -0.490625t + t2 = 3.5625 The t term is -0.490625t. Take half its coefficient (-0.2453125). Square it (0.06017822266) and add it to both sides. Add '0.06017822266' to each side of the equation. -0.490625t + 0.06017822266 + t2 = 3.5625 + 0.06017822266 Reorder the terms: 0.06017822266 + -0.490625t + t2 = 3.5625 + 0.06017822266 Combine like terms: 3.5625 + 0.06017822266 = 3.62267822266 0.06017822266 + -0.490625t + t2 = 3.62267822266 Factor a perfect square on the left side: (t + -0.2453125)(t + -0.2453125) = 3.62267822266 Calculate the square root of the right side: 1.90333345 Break this problem into two subproblems by setting (t + -0.2453125) equal to 1.90333345 and -1.90333345.Subproblem 1
t + -0.2453125 = 1.90333345 Simplifying t + -0.2453125 = 1.90333345 Reorder the terms: -0.2453125 + t = 1.90333345 Solving -0.2453125 + t = 1.90333345 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.2453125' to each side of the equation. -0.2453125 + 0.2453125 + t = 1.90333345 + 0.2453125 Combine like terms: -0.2453125 + 0.2453125 = 0.0000000 0.0000000 + t = 1.90333345 + 0.2453125 t = 1.90333345 + 0.2453125 Combine like terms: 1.90333345 + 0.2453125 = 2.14864595 t = 2.14864595 Simplifying t = 2.14864595Subproblem 2
t + -0.2453125 = -1.90333345 Simplifying t + -0.2453125 = -1.90333345 Reorder the terms: -0.2453125 + t = -1.90333345 Solving -0.2453125 + t = -1.90333345 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.2453125' to each side of the equation. -0.2453125 + 0.2453125 + t = -1.90333345 + 0.2453125 Combine like terms: -0.2453125 + 0.2453125 = 0.0000000 0.0000000 + t = -1.90333345 + 0.2453125 t = -1.90333345 + 0.2453125 Combine like terms: -1.90333345 + 0.2453125 = -1.65802095 t = -1.65802095 Simplifying t = -1.65802095Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.14864595, -1.65802095}
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