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Simplifying -0.2t2 + 5.2t = 17.6 Reorder the terms: 5.2t + -0.2t2 = 17.6 Solving 5.2t + -0.2t2 = 17.6 Solving for variable 't'. Reorder the terms: -17.6 + 5.2t + -0.2t2 = 17.6 + -17.6 Combine like terms: 17.6 + -17.6 = 0.0 -17.6 + 5.2t + -0.2t2 = 0.0 Begin completing the square. Divide all terms by -0.2 the coefficient of the squared term: Divide each side by '-0.2'. 88 + -26t + t2 = 0 Move the constant term to the right: Add '-88' to each side of the equation. 88 + -26t + -88 + t2 = 0 + -88 Reorder the terms: 88 + -88 + -26t + t2 = 0 + -88 Combine like terms: 88 + -88 = 0 0 + -26t + t2 = 0 + -88 -26t + t2 = 0 + -88 Combine like terms: 0 + -88 = -88 -26t + t2 = -88 The t term is -26t. Take half its coefficient (-13). Square it (169) and add it to both sides. Add '169' to each side of the equation. -26t + 169 + t2 = -88 + 169 Reorder the terms: 169 + -26t + t2 = -88 + 169 Combine like terms: -88 + 169 = 81 169 + -26t + t2 = 81 Factor a perfect square on the left side: (t + -13)(t + -13) = 81 Calculate the square root of the right side: 9 Break this problem into two subproblems by setting (t + -13) equal to 9 and -9.Subproblem 1
t + -13 = 9 Simplifying t + -13 = 9 Reorder the terms: -13 + t = 9 Solving -13 + t = 9 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '13' to each side of the equation. -13 + 13 + t = 9 + 13 Combine like terms: -13 + 13 = 0 0 + t = 9 + 13 t = 9 + 13 Combine like terms: 9 + 13 = 22 t = 22 Simplifying t = 22Subproblem 2
t + -13 = -9 Simplifying t + -13 = -9 Reorder the terms: -13 + t = -9 Solving -13 + t = -9 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '13' to each side of the equation. -13 + 13 + t = -9 + 13 Combine like terms: -13 + 13 = 0 0 + t = -9 + 13 t = -9 + 13 Combine like terms: -9 + 13 = 4 t = 4 Simplifying t = 4Solution
The solution to the problem is based on the solutions from the subproblems. t = {22, 4}
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