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Simplifying 11 = 9t + -0.3t2 Solving 11 = 9t + -0.3t2 Solving for variable 't'. Reorder the terms: 11 + -9t + 0.3t2 = 9t + -9t + -0.3t2 + 0.3t2 Combine like terms: 9t + -9t = 0 11 + -9t + 0.3t2 = 0 + -0.3t2 + 0.3t2 11 + -9t + 0.3t2 = -0.3t2 + 0.3t2 Combine like terms: -0.3t2 + 0.3t2 = 0.0 11 + -9t + 0.3t2 = 0.0 Begin completing the square. Divide all terms by 0.3 the coefficient of the squared term: Divide each side by '0.3'. 36.66666667 + -30t + t2 = 0 Move the constant term to the right: Add '-36.66666667' to each side of the equation. 36.66666667 + -30t + -36.66666667 + t2 = 0 + -36.66666667 Reorder the terms: 36.66666667 + -36.66666667 + -30t + t2 = 0 + -36.66666667 Combine like terms: 36.66666667 + -36.66666667 = 0.00000000 0.00000000 + -30t + t2 = 0 + -36.66666667 -30t + t2 = 0 + -36.66666667 Combine like terms: 0 + -36.66666667 = -36.66666667 -30t + t2 = -36.66666667 The t term is -30t. Take half its coefficient (-15). Square it (225) and add it to both sides. Add '225' to each side of the equation. -30t + 225 + t2 = -36.66666667 + 225 Reorder the terms: 225 + -30t + t2 = -36.66666667 + 225 Combine like terms: -36.66666667 + 225 = 188.33333333 225 + -30t + t2 = 188.33333333 Factor a perfect square on the left side: (t + -15)(t + -15) = 188.33333333 Calculate the square root of the right side: 13.723459233 Break this problem into two subproblems by setting (t + -15) equal to 13.723459233 and -13.723459233.Subproblem 1
t + -15 = 13.723459233 Simplifying t + -15 = 13.723459233 Reorder the terms: -15 + t = 13.723459233 Solving -15 + t = 13.723459233 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '15' to each side of the equation. -15 + 15 + t = 13.723459233 + 15 Combine like terms: -15 + 15 = 0 0 + t = 13.723459233 + 15 t = 13.723459233 + 15 Combine like terms: 13.723459233 + 15 = 28.723459233 t = 28.723459233 Simplifying t = 28.723459233Subproblem 2
t + -15 = -13.723459233 Simplifying t + -15 = -13.723459233 Reorder the terms: -15 + t = -13.723459233 Solving -15 + t = -13.723459233 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '15' to each side of the equation. -15 + 15 + t = -13.723459233 + 15 Combine like terms: -15 + 15 = 0 0 + t = -13.723459233 + 15 t = -13.723459233 + 15 Combine like terms: -13.723459233 + 15 = 1.276540767 t = 1.276540767 Simplifying t = 1.276540767Solution
The solution to the problem is based on the solutions from the subproblems. t = {28.723459233, 1.276540767}
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