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Simplifying 7(18 + -1t) * 2t = -39 Reorder the terms for easier multiplication: 7 * 2t(18 + -1t) = -39 Multiply 7 * 2 14t(18 + -1t) = -39 (18 * 14t + -1t * 14t) = -39 (252t + -14t2) = -39 Solving 252t + -14t2 = -39 Solving for variable 't'. Reorder the terms: 39 + 252t + -14t2 = -39 + 39 Combine like terms: -39 + 39 = 0 39 + 252t + -14t2 = 0 Begin completing the square. Divide all terms by -14 the coefficient of the squared term: Divide each side by '-14'. -2.785714286 + -18t + t2 = 0 Move the constant term to the right: Add '2.785714286' to each side of the equation. -2.785714286 + -18t + 2.785714286 + t2 = 0 + 2.785714286 Reorder the terms: -2.785714286 + 2.785714286 + -18t + t2 = 0 + 2.785714286 Combine like terms: -2.785714286 + 2.785714286 = 0.000000000 0.000000000 + -18t + t2 = 0 + 2.785714286 -18t + t2 = 0 + 2.785714286 Combine like terms: 0 + 2.785714286 = 2.785714286 -18t + t2 = 2.785714286 The t term is -18t. Take half its coefficient (-9). Square it (81) and add it to both sides. Add '81' to each side of the equation. -18t + 81 + t2 = 2.785714286 + 81 Reorder the terms: 81 + -18t + t2 = 2.785714286 + 81 Combine like terms: 2.785714286 + 81 = 83.785714286 81 + -18t + t2 = 83.785714286 Factor a perfect square on the left side: (t + -9)(t + -9) = 83.785714286 Calculate the square root of the right side: 9.153453681 Break this problem into two subproblems by setting (t + -9) equal to 9.153453681 and -9.153453681.Subproblem 1
t + -9 = 9.153453681 Simplifying t + -9 = 9.153453681 Reorder the terms: -9 + t = 9.153453681 Solving -9 + t = 9.153453681 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + t = 9.153453681 + 9 Combine like terms: -9 + 9 = 0 0 + t = 9.153453681 + 9 t = 9.153453681 + 9 Combine like terms: 9.153453681 + 9 = 18.153453681 t = 18.153453681 Simplifying t = 18.153453681Subproblem 2
t + -9 = -9.153453681 Simplifying t + -9 = -9.153453681 Reorder the terms: -9 + t = -9.153453681 Solving -9 + t = -9.153453681 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + t = -9.153453681 + 9 Combine like terms: -9 + 9 = 0 0 + t = -9.153453681 + 9 t = -9.153453681 + 9 Combine like terms: -9.153453681 + 9 = -0.153453681 t = -0.153453681 Simplifying t = -0.153453681Solution
The solution to the problem is based on the solutions from the subproblems. t = {18.153453681, -0.153453681}
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