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Simplifying 4t(t + -6) = -9 Reorder the terms: 4t(-6 + t) = -9 (-6 * 4t + t * 4t) = -9 (-24t + 4t2) = -9 Solving -24t + 4t2 = -9 Solving for variable 't'. Reorder the terms: 9 + -24t + 4t2 = -9 + 9 Combine like terms: -9 + 9 = 0 9 + -24t + 4t2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 2.25 + -6t + t2 = 0 Move the constant term to the right: Add '-2.25' to each side of the equation. 2.25 + -6t + -2.25 + t2 = 0 + -2.25 Reorder the terms: 2.25 + -2.25 + -6t + t2 = 0 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + -6t + t2 = 0 + -2.25 -6t + t2 = 0 + -2.25 Combine like terms: 0 + -2.25 = -2.25 -6t + t2 = -2.25 The t term is -6t. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6t + 9 + t2 = -2.25 + 9 Reorder the terms: 9 + -6t + t2 = -2.25 + 9 Combine like terms: -2.25 + 9 = 6.75 9 + -6t + t2 = 6.75 Factor a perfect square on the left side: (t + -3)(t + -3) = 6.75 Calculate the square root of the right side: 2.598076211 Break this problem into two subproblems by setting (t + -3) equal to 2.598076211 and -2.598076211.Subproblem 1
t + -3 = 2.598076211 Simplifying t + -3 = 2.598076211 Reorder the terms: -3 + t = 2.598076211 Solving -3 + t = 2.598076211 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + t = 2.598076211 + 3 Combine like terms: -3 + 3 = 0 0 + t = 2.598076211 + 3 t = 2.598076211 + 3 Combine like terms: 2.598076211 + 3 = 5.598076211 t = 5.598076211 Simplifying t = 5.598076211Subproblem 2
t + -3 = -2.598076211 Simplifying t + -3 = -2.598076211 Reorder the terms: -3 + t = -2.598076211 Solving -3 + t = -2.598076211 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + t = -2.598076211 + 3 Combine like terms: -3 + 3 = 0 0 + t = -2.598076211 + 3 t = -2.598076211 + 3 Combine like terms: -2.598076211 + 3 = 0.401923789 t = 0.401923789 Simplifying t = 0.401923789Solution
The solution to the problem is based on the solutions from the subproblems. t = {5.598076211, 0.401923789}
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