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Simplifying -0.2t2 + 5t + -17 = 0 Reorder the terms: -17 + 5t + -0.2t2 = 0 Solving -17 + 5t + -0.2t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by -0.2 the coefficient of the squared term: Divide each side by '-0.2'. 85 + -25t + t2 = 0 Move the constant term to the right: Add '-85' to each side of the equation. 85 + -25t + -85 + t2 = 0 + -85 Reorder the terms: 85 + -85 + -25t + t2 = 0 + -85 Combine like terms: 85 + -85 = 0 0 + -25t + t2 = 0 + -85 -25t + t2 = 0 + -85 Combine like terms: 0 + -85 = -85 -25t + t2 = -85 The t term is -25t. Take half its coefficient (-12.5). Square it (156.25) and add it to both sides. Add '156.25' to each side of the equation. -25t + 156.25 + t2 = -85 + 156.25 Reorder the terms: 156.25 + -25t + t2 = -85 + 156.25 Combine like terms: -85 + 156.25 = 71.25 156.25 + -25t + t2 = 71.25 Factor a perfect square on the left side: (t + -12.5)(t + -12.5) = 71.25 Calculate the square root of the right side: 8.440971508 Break this problem into two subproblems by setting (t + -12.5) equal to 8.440971508 and -8.440971508.Subproblem 1
t + -12.5 = 8.440971508 Simplifying t + -12.5 = 8.440971508 Reorder the terms: -12.5 + t = 8.440971508 Solving -12.5 + t = 8.440971508 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '12.5' to each side of the equation. -12.5 + 12.5 + t = 8.440971508 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + t = 8.440971508 + 12.5 t = 8.440971508 + 12.5 Combine like terms: 8.440971508 + 12.5 = 20.940971508 t = 20.940971508 Simplifying t = 20.940971508Subproblem 2
t + -12.5 = -8.440971508 Simplifying t + -12.5 = -8.440971508 Reorder the terms: -12.5 + t = -8.440971508 Solving -12.5 + t = -8.440971508 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '12.5' to each side of the equation. -12.5 + 12.5 + t = -8.440971508 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + t = -8.440971508 + 12.5 t = -8.440971508 + 12.5 Combine like terms: -8.440971508 + 12.5 = 4.059028492 t = 4.059028492 Simplifying t = 4.059028492Solution
The solution to the problem is based on the solutions from the subproblems. t = {20.940971508, 4.059028492}
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