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Simplifying 3t2 + 3t + -80 = 0 Reorder the terms: -80 + 3t + 3t2 = 0 Solving -80 + 3t + 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'. -26.66666667 + t + t2 = 0 Move the constant term to the right: Add '26.66666667' to each side of the equation. -26.66666667 + t + 26.66666667 + t2 = 0 + 26.66666667 Reorder the terms: -26.66666667 + 26.66666667 + t + t2 = 0 + 26.66666667 Combine like terms: -26.66666667 + 26.66666667 = 0.00000000 0.00000000 + t + t2 = 0 + 26.66666667 t + t2 = 0 + 26.66666667 Combine like terms: 0 + 26.66666667 = 26.66666667 t + t2 = 26.66666667 The t term is t. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. + 0.25 + t2 = 26.66666667 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + t2 = 26.66666667 + 0.25 Combine like terms: 26.66666667 + 0.25 = 26.91666667 1.25 + t2 = 26.91666667 Factor a perfect square on the left side: (t + 0.5)(t + 0.5) = 26.91666667 Calculate the square root of the right side: 5.188127472 Break this problem into two subproblems by setting (t + 0.5) equal to 5.188127472 and -5.188127472.Subproblem 1
t + 0.5 = 5.188127472 Simplifying t + 0.5 = 5.188127472 Reorder the terms: 0.5 + t = 5.188127472 Solving 0.5 + t = 5.188127472 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + t = 5.188127472 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + t = 5.188127472 + -0.5 t = 5.188127472 + -0.5 Combine like terms: 5.188127472 + -0.5 = 4.688127472 t = 4.688127472 Simplifying t = 4.688127472Subproblem 2
t + 0.5 = -5.188127472 Simplifying t + 0.5 = -5.188127472 Reorder the terms: 0.5 + t = -5.188127472 Solving 0.5 + t = -5.188127472 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + t = -5.188127472 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + t = -5.188127472 + -0.5 t = -5.188127472 + -0.5 Combine like terms: -5.188127472 + -0.5 = -5.688127472 t = -5.688127472 Simplifying t = -5.688127472Solution
The solution to the problem is based on the solutions from the subproblems. t = {4.688127472, -5.688127472}
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