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Simplifying -9t(t + -2) = 4(t + -15) Reorder the terms: -9t(-2 + t) = 4(t + -15) (-2 * -9t + t * -9t) = 4(t + -15) (18t + -9t2) = 4(t + -15) Reorder the terms: 18t + -9t2 = 4(-15 + t) 18t + -9t2 = (-15 * 4 + t * 4) 18t + -9t2 = (-60 + 4t) Solving 18t + -9t2 = -60 + 4t Solving for variable 't'. Reorder the terms: 60 + 18t + -4t + -9t2 = -60 + 4t + 60 + -4t Combine like terms: 18t + -4t = 14t 60 + 14t + -9t2 = -60 + 4t + 60 + -4t Reorder the terms: 60 + 14t + -9t2 = -60 + 60 + 4t + -4t Combine like terms: -60 + 60 = 0 60 + 14t + -9t2 = 0 + 4t + -4t 60 + 14t + -9t2 = 4t + -4t Combine like terms: 4t + -4t = 0 60 + 14t + -9t2 = 0 Begin completing the square. Divide all terms by -9 the coefficient of the squared term: Divide each side by '-9'. -6.666666667 + -1.555555556t + t2 = 0 Move the constant term to the right: Add '6.666666667' to each side of the equation. -6.666666667 + -1.555555556t + 6.666666667 + t2 = 0 + 6.666666667 Reorder the terms: -6.666666667 + 6.666666667 + -1.555555556t + t2 = 0 + 6.666666667 Combine like terms: -6.666666667 + 6.666666667 = 0.000000000 0.000000000 + -1.555555556t + t2 = 0 + 6.666666667 -1.555555556t + t2 = 0 + 6.666666667 Combine like terms: 0 + 6.666666667 = 6.666666667 -1.555555556t + t2 = 6.666666667 The t term is -1.555555556t. Take half its coefficient (-0.777777778). Square it (0.6049382720) and add it to both sides. Add '0.6049382720' to each side of the equation. -1.555555556t + 0.6049382720 + t2 = 6.666666667 + 0.6049382720 Reorder the terms: 0.6049382720 + -1.555555556t + t2 = 6.666666667 + 0.6049382720 Combine like terms: 6.666666667 + 0.6049382720 = 7.271604939 0.6049382720 + -1.555555556t + t2 = 7.271604939 Factor a perfect square on the left side: (t + -0.777777778)(t + -0.777777778) = 7.271604939 Calculate the square root of the right side: 2.696591356 Break this problem into two subproblems by setting (t + -0.777777778) equal to 2.696591356 and -2.696591356.Subproblem 1
t + -0.777777778 = 2.696591356 Simplifying t + -0.777777778 = 2.696591356 Reorder the terms: -0.777777778 + t = 2.696591356 Solving -0.777777778 + t = 2.696591356 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.777777778' to each side of the equation. -0.777777778 + 0.777777778 + t = 2.696591356 + 0.777777778 Combine like terms: -0.777777778 + 0.777777778 = 0.000000000 0.000000000 + t = 2.696591356 + 0.777777778 t = 2.696591356 + 0.777777778 Combine like terms: 2.696591356 + 0.777777778 = 3.474369134 t = 3.474369134 Simplifying t = 3.474369134Subproblem 2
t + -0.777777778 = -2.696591356 Simplifying t + -0.777777778 = -2.696591356 Reorder the terms: -0.777777778 + t = -2.696591356 Solving -0.777777778 + t = -2.696591356 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.777777778' to each side of the equation. -0.777777778 + 0.777777778 + t = -2.696591356 + 0.777777778 Combine like terms: -0.777777778 + 0.777777778 = 0.000000000 0.000000000 + t = -2.696591356 + 0.777777778 t = -2.696591356 + 0.777777778 Combine like terms: -2.696591356 + 0.777777778 = -1.918813578 t = -1.918813578 Simplifying t = -1.918813578Solution
The solution to the problem is based on the solutions from the subproblems. t = {3.474369134, -1.918813578}
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