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Simplifying 64.3 = -0.5t2 + 1.8t + 67.8 Reorder the terms: 64.3 = 67.8 + 1.8t + -0.5t2 Solving 64.3 = 67.8 + 1.8t + -0.5t2 Solving for variable 't'. Combine like terms: 64.3 + -67.8 = -3.5 -3.5 + -1.8t + 0.5t2 = 67.8 + 1.8t + -0.5t2 + -67.8 + -1.8t + 0.5t2 Reorder the terms: -3.5 + -1.8t + 0.5t2 = 67.8 + -67.8 + 1.8t + -1.8t + -0.5t2 + 0.5t2 Combine like terms: 67.8 + -67.8 = 0.0 -3.5 + -1.8t + 0.5t2 = 0.0 + 1.8t + -1.8t + -0.5t2 + 0.5t2 -3.5 + -1.8t + 0.5t2 = 1.8t + -1.8t + -0.5t2 + 0.5t2 Combine like terms: 1.8t + -1.8t = 0.0 -3.5 + -1.8t + 0.5t2 = 0.0 + -0.5t2 + 0.5t2 -3.5 + -1.8t + 0.5t2 = -0.5t2 + 0.5t2 Combine like terms: -0.5t2 + 0.5t2 = 0.0 -3.5 + -1.8t + 0.5t2 = 0.0 Begin completing the square. Divide all terms by 0.5 the coefficient of the squared term: Divide each side by '0.5'. -7 + -3.6t + t2 = 0 Move the constant term to the right: Add '7' to each side of the equation. -7 + -3.6t + 7 + t2 = 0 + 7 Reorder the terms: -7 + 7 + -3.6t + t2 = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -3.6t + t2 = 0 + 7 -3.6t + t2 = 0 + 7 Combine like terms: 0 + 7 = 7 -3.6t + t2 = 7 The t term is -3.6t. Take half its coefficient (-1.8). Square it (3.24) and add it to both sides. Add '3.24' to each side of the equation. -3.6t + 3.24 + t2 = 7 + 3.24 Reorder the terms: 3.24 + -3.6t + t2 = 7 + 3.24 Combine like terms: 7 + 3.24 = 10.24 3.24 + -3.6t + t2 = 10.24 Factor a perfect square on the left side: (t + -1.8)(t + -1.8) = 10.24 Calculate the square root of the right side: 3.2 Break this problem into two subproblems by setting (t + -1.8) equal to 3.2 and -3.2.Subproblem 1
t + -1.8 = 3.2 Simplifying t + -1.8 = 3.2 Reorder the terms: -1.8 + t = 3.2 Solving -1.8 + t = 3.2 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.8' to each side of the equation. -1.8 + 1.8 + t = 3.2 + 1.8 Combine like terms: -1.8 + 1.8 = 0.0 0.0 + t = 3.2 + 1.8 t = 3.2 + 1.8 Combine like terms: 3.2 + 1.8 = 5 t = 5 Simplifying t = 5Subproblem 2
t + -1.8 = -3.2 Simplifying t + -1.8 = -3.2 Reorder the terms: -1.8 + t = -3.2 Solving -1.8 + t = -3.2 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.8' to each side of the equation. -1.8 + 1.8 + t = -3.2 + 1.8 Combine like terms: -1.8 + 1.8 = 0.0 0.0 + t = -3.2 + 1.8 t = -3.2 + 1.8 Combine like terms: -3.2 + 1.8 = -1.4 t = -1.4 Simplifying t = -1.4Solution
The solution to the problem is based on the solutions from the subproblems. t = {5, -1.4}
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