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Simplifying 3t2 + -6t + -8 = 0 Reorder the terms: -8 + -6t + 3t2 = 0 Solving -8 + -6t + 3t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -2.666666667 + -2t + t2 = 0 Move the constant term to the right: Add '2.666666667' to each side of the equation. -2.666666667 + -2t + 2.666666667 + t2 = 0 + 2.666666667 Reorder the terms: -2.666666667 + 2.666666667 + -2t + t2 = 0 + 2.666666667 Combine like terms: -2.666666667 + 2.666666667 = 0.000000000 0.000000000 + -2t + t2 = 0 + 2.666666667 -2t + t2 = 0 + 2.666666667 Combine like terms: 0 + 2.666666667 = 2.666666667 -2t + t2 = 2.666666667 The t term is -2t. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2t + 1 + t2 = 2.666666667 + 1 Reorder the terms: 1 + -2t + t2 = 2.666666667 + 1 Combine like terms: 2.666666667 + 1 = 3.666666667 1 + -2t + t2 = 3.666666667 Factor a perfect square on the left side: (t + -1)(t + -1) = 3.666666667 Calculate the square root of the right side: 1.914854216 Break this problem into two subproblems by setting (t + -1) equal to 1.914854216 and -1.914854216.Subproblem 1
t + -1 = 1.914854216 Simplifying t + -1 = 1.914854216 Reorder the terms: -1 + t = 1.914854216 Solving -1 + t = 1.914854216 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + t = 1.914854216 + 1 Combine like terms: -1 + 1 = 0 0 + t = 1.914854216 + 1 t = 1.914854216 + 1 Combine like terms: 1.914854216 + 1 = 2.914854216 t = 2.914854216 Simplifying t = 2.914854216Subproblem 2
t + -1 = -1.914854216 Simplifying t + -1 = -1.914854216 Reorder the terms: -1 + t = -1.914854216 Solving -1 + t = -1.914854216 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + t = -1.914854216 + 1 Combine like terms: -1 + 1 = 0 0 + t = -1.914854216 + 1 t = -1.914854216 + 1 Combine like terms: -1.914854216 + 1 = -0.914854216 t = -0.914854216 Simplifying t = -0.914854216Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.914854216, -0.914854216}
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