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Simplifying 0 = 3t2 + -23t + -6 Reorder the terms: 0 = -6 + -23t + 3t2 Solving 0 = -6 + -23t + 3t2 Solving for variable 't'. Combine like terms: 0 + 6 = 6 6 + 23t + -3t2 = -6 + -23t + 3t2 + 6 + 23t + -3t2 Reorder the terms: 6 + 23t + -3t2 = -6 + 6 + -23t + 23t + 3t2 + -3t2 Combine like terms: -6 + 6 = 0 6 + 23t + -3t2 = 0 + -23t + 23t + 3t2 + -3t2 6 + 23t + -3t2 = -23t + 23t + 3t2 + -3t2 Combine like terms: -23t + 23t = 0 6 + 23t + -3t2 = 0 + 3t2 + -3t2 6 + 23t + -3t2 = 3t2 + -3t2 Combine like terms: 3t2 + -3t2 = 0 6 + 23t + -3t2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. -2 + -7.666666667t + t2 = 0 Move the constant term to the right: Add '2' to each side of the equation. -2 + -7.666666667t + 2 + t2 = 0 + 2 Reorder the terms: -2 + 2 + -7.666666667t + t2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -7.666666667t + t2 = 0 + 2 -7.666666667t + t2 = 0 + 2 Combine like terms: 0 + 2 = 2 -7.666666667t + t2 = 2 The t term is -7.666666667t. Take half its coefficient (-3.833333334). Square it (14.69444445) and add it to both sides. Add '14.69444445' to each side of the equation. -7.666666667t + 14.69444445 + t2 = 2 + 14.69444445 Reorder the terms: 14.69444445 + -7.666666667t + t2 = 2 + 14.69444445 Combine like terms: 2 + 14.69444445 = 16.69444445 14.69444445 + -7.666666667t + t2 = 16.69444445 Factor a perfect square on the left side: (t + -3.833333334)(t + -3.833333334) = 16.69444445 Calculate the square root of the right side: 4.085883558 Break this problem into two subproblems by setting (t + -3.833333334) equal to 4.085883558 and -4.085883558.Subproblem 1
t + -3.833333334 = 4.085883558 Simplifying t + -3.833333334 = 4.085883558 Reorder the terms: -3.833333334 + t = 4.085883558 Solving -3.833333334 + t = 4.085883558 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3.833333334' to each side of the equation. -3.833333334 + 3.833333334 + t = 4.085883558 + 3.833333334 Combine like terms: -3.833333334 + 3.833333334 = 0.000000000 0.000000000 + t = 4.085883558 + 3.833333334 t = 4.085883558 + 3.833333334 Combine like terms: 4.085883558 + 3.833333334 = 7.919216892 t = 7.919216892 Simplifying t = 7.919216892Subproblem 2
t + -3.833333334 = -4.085883558 Simplifying t + -3.833333334 = -4.085883558 Reorder the terms: -3.833333334 + t = -4.085883558 Solving -3.833333334 + t = -4.085883558 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3.833333334' to each side of the equation. -3.833333334 + 3.833333334 + t = -4.085883558 + 3.833333334 Combine like terms: -3.833333334 + 3.833333334 = 0.000000000 0.000000000 + t = -4.085883558 + 3.833333334 t = -4.085883558 + 3.833333334 Combine like terms: -4.085883558 + 3.833333334 = -0.252550224 t = -0.252550224 Simplifying t = -0.252550224Solution
The solution to the problem is based on the solutions from the subproblems. t = {7.919216892, -0.252550224}
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