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Simplifying (2t2 + 7t + -6) + -1(3t2 + -11t + -9) = 0 Reorder the terms: (-6 + 7t + 2t2) + -1(3t2 + -11t + -9) = 0 Remove parenthesis around (-6 + 7t + 2t2) -6 + 7t + 2t2 + -1(3t2 + -11t + -9) = 0 Reorder the terms: -6 + 7t + 2t2 + -1(-9 + -11t + 3t2) = 0 -6 + 7t + 2t2 + (-9 * -1 + -11t * -1 + 3t2 * -1) = 0 -6 + 7t + 2t2 + (9 + 11t + -3t2) = 0 Reorder the terms: -6 + 9 + 7t + 11t + 2t2 + -3t2 = 0 Combine like terms: -6 + 9 = 3 3 + 7t + 11t + 2t2 + -3t2 = 0 Combine like terms: 7t + 11t = 18t 3 + 18t + 2t2 + -3t2 = 0 Combine like terms: 2t2 + -3t2 = -1t2 3 + 18t + -1t2 = 0 Solving 3 + 18t + -1t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -3 + -18t + t2 = 0 Move the constant term to the right: Add '3' to each side of the equation. -3 + -18t + 3 + t2 = 0 + 3 Reorder the terms: -3 + 3 + -18t + t2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -18t + t2 = 0 + 3 -18t + t2 = 0 + 3 Combine like terms: 0 + 3 = 3 -18t + t2 = 3 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 = 3 + 81 Reorder the terms: 81 + -18t + t2 = 3 + 81 Combine like terms: 3 + 81 = 84 81 + -18t + t2 = 84 Factor a perfect square on the left side: (t + -9)(t + -9) = 84 Calculate the square root of the right side: 9.16515139 Break this problem into two subproblems by setting (t + -9) equal to 9.16515139 and -9.16515139.Subproblem 1
t + -9 = 9.16515139 Simplifying t + -9 = 9.16515139 Reorder the terms: -9 + t = 9.16515139 Solving -9 + t = 9.16515139 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 = 9.16515139 + 9 Combine like terms: -9 + 9 = 0 0 + t = 9.16515139 + 9 t = 9.16515139 + 9 Combine like terms: 9.16515139 + 9 = 18.16515139 t = 18.16515139 Simplifying t = 18.16515139Subproblem 2
t + -9 = -9.16515139 Simplifying t + -9 = -9.16515139 Reorder the terms: -9 + t = -9.16515139 Solving -9 + t = -9.16515139 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 = -9.16515139 + 9 Combine like terms: -9 + 9 = 0 0 + t = -9.16515139 + 9 t = -9.16515139 + 9 Combine like terms: -9.16515139 + 9 = -0.16515139 t = -0.16515139 Simplifying t = -0.16515139Solution
The solution to the problem is based on the solutions from the subproblems. t = {18.16515139, -0.16515139}
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