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Simplifying 3t2 + 9t + -28 = 0 Reorder the terms: -28 + 9t + 3t2 = 0 Solving -28 + 9t + 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'. -9.333333333 + 3t + t2 = 0 Move the constant term to the right: Add '9.333333333' to each side of the equation. -9.333333333 + 3t + 9.333333333 + t2 = 0 + 9.333333333 Reorder the terms: -9.333333333 + 9.333333333 + 3t + t2 = 0 + 9.333333333 Combine like terms: -9.333333333 + 9.333333333 = 0.000000000 0.000000000 + 3t + t2 = 0 + 9.333333333 3t + t2 = 0 + 9.333333333 Combine like terms: 0 + 9.333333333 = 9.333333333 3t + t2 = 9.333333333 The t term is 3t. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3t + 2.25 + t2 = 9.333333333 + 2.25 Reorder the terms: 2.25 + 3t + t2 = 9.333333333 + 2.25 Combine like terms: 9.333333333 + 2.25 = 11.583333333 2.25 + 3t + t2 = 11.583333333 Factor a perfect square on the left side: (t + 1.5)(t + 1.5) = 11.583333333 Calculate the square root of the right side: 3.403429643 Break this problem into two subproblems by setting (t + 1.5) equal to 3.403429643 and -3.403429643.Subproblem 1
t + 1.5 = 3.403429643 Simplifying t + 1.5 = 3.403429643 Reorder the terms: 1.5 + t = 3.403429643 Solving 1.5 + t = 3.403429643 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + t = 3.403429643 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + t = 3.403429643 + -1.5 t = 3.403429643 + -1.5 Combine like terms: 3.403429643 + -1.5 = 1.903429643 t = 1.903429643 Simplifying t = 1.903429643Subproblem 2
t + 1.5 = -3.403429643 Simplifying t + 1.5 = -3.403429643 Reorder the terms: 1.5 + t = -3.403429643 Solving 1.5 + t = -3.403429643 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + t = -3.403429643 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + t = -3.403429643 + -1.5 t = -3.403429643 + -1.5 Combine like terms: -3.403429643 + -1.5 = -4.903429643 t = -4.903429643 Simplifying t = -4.903429643Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.903429643, -4.903429643}
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