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Simplifying 132t + -5.5t2 = 440 Solving 132t + -5.5t2 = 440 Solving for variable 't'. Reorder the terms: -440 + 132t + -5.5t2 = 440 + -440 Combine like terms: 440 + -440 = 0 -440 + 132t + -5.5t2 = 0 Begin completing the square. Divide all terms by -5.5 the coefficient of the squared term: Divide each side by '-5.5'. 80 + -24t + t2 = 0 Move the constant term to the right: Add '-80' to each side of the equation. 80 + -24t + -80 + t2 = 0 + -80 Reorder the terms: 80 + -80 + -24t + t2 = 0 + -80 Combine like terms: 80 + -80 = 0 0 + -24t + t2 = 0 + -80 -24t + t2 = 0 + -80 Combine like terms: 0 + -80 = -80 -24t + t2 = -80 The t term is -24t. Take half its coefficient (-12). Square it (144) and add it to both sides. Add '144' to each side of the equation. -24t + 144 + t2 = -80 + 144 Reorder the terms: 144 + -24t + t2 = -80 + 144 Combine like terms: -80 + 144 = 64 144 + -24t + t2 = 64 Factor a perfect square on the left side: (t + -12)(t + -12) = 64 Calculate the square root of the right side: 8 Break this problem into two subproblems by setting (t + -12) equal to 8 and -8.Subproblem 1
t + -12 = 8 Simplifying t + -12 = 8 Reorder the terms: -12 + t = 8 Solving -12 + t = 8 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + t = 8 + 12 Combine like terms: -12 + 12 = 0 0 + t = 8 + 12 t = 8 + 12 Combine like terms: 8 + 12 = 20 t = 20 Simplifying t = 20Subproblem 2
t + -12 = -8 Simplifying t + -12 = -8 Reorder the terms: -12 + t = -8 Solving -12 + t = -8 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + t = -8 + 12 Combine like terms: -12 + 12 = 0 0 + t = -8 + 12 t = -8 + 12 Combine like terms: -8 + 12 = 4 t = 4 Simplifying t = 4Solution
The solution to the problem is based on the solutions from the subproblems. t = {20, 4}
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