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Simplifying -0.08t2 + 1.6t + 20 = 9 Reorder the terms: 20 + 1.6t + -0.08t2 = 9 Solving 20 + 1.6t + -0.08t2 = 9 Solving for variable 't'. Reorder the terms: 20 + -9 + 1.6t + -0.08t2 = 9 + -9 Combine like terms: 20 + -9 = 11 11 + 1.6t + -0.08t2 = 9 + -9 Combine like terms: 9 + -9 = 0 11 + 1.6t + -0.08t2 = 0 Begin completing the square. Divide all terms by -0.08 the coefficient of the squared term: Divide each side by '-0.08'. -137.5 + -20t + t2 = 0 Move the constant term to the right: Add '137.5' to each side of the equation. -137.5 + -20t + 137.5 + t2 = 0 + 137.5 Reorder the terms: -137.5 + 137.5 + -20t + t2 = 0 + 137.5 Combine like terms: -137.5 + 137.5 = 0.0 0.0 + -20t + t2 = 0 + 137.5 -20t + t2 = 0 + 137.5 Combine like terms: 0 + 137.5 = 137.5 -20t + t2 = 137.5 The t term is -20t. Take half its coefficient (-10). Square it (100) and add it to both sides. Add '100' to each side of the equation. -20t + 100 + t2 = 137.5 + 100 Reorder the terms: 100 + -20t + t2 = 137.5 + 100 Combine like terms: 137.5 + 100 = 237.5 100 + -20t + t2 = 237.5 Factor a perfect square on the left side: (t + -10)(t + -10) = 237.5 Calculate the square root of the right side: 15.411035007 Break this problem into two subproblems by setting (t + -10) equal to 15.411035007 and -15.411035007.Subproblem 1
t + -10 = 15.411035007 Simplifying t + -10 = 15.411035007 Reorder the terms: -10 + t = 15.411035007 Solving -10 + t = 15.411035007 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + t = 15.411035007 + 10 Combine like terms: -10 + 10 = 0 0 + t = 15.411035007 + 10 t = 15.411035007 + 10 Combine like terms: 15.411035007 + 10 = 25.411035007 t = 25.411035007 Simplifying t = 25.411035007Subproblem 2
t + -10 = -15.411035007 Simplifying t + -10 = -15.411035007 Reorder the terms: -10 + t = -15.411035007 Solving -10 + t = -15.411035007 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + t = -15.411035007 + 10 Combine like terms: -10 + 10 = 0 0 + t = -15.411035007 + 10 t = -15.411035007 + 10 Combine like terms: -15.411035007 + 10 = -5.411035007 t = -5.411035007 Simplifying t = -5.411035007Solution
The solution to the problem is based on the solutions from the subproblems. t = {25.411035007, -5.411035007}
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