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Simplifying 3t2 + 6t + -43 = 0 Reorder the terms: -43 + 6t + 3t2 = 0 Solving -43 + 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'. -14.33333333 + 2t + t2 = 0 Move the constant term to the right: Add '14.33333333' to each side of the equation. -14.33333333 + 2t + 14.33333333 + t2 = 0 + 14.33333333 Reorder the terms: -14.33333333 + 14.33333333 + 2t + t2 = 0 + 14.33333333 Combine like terms: -14.33333333 + 14.33333333 = 0.00000000 0.00000000 + 2t + t2 = 0 + 14.33333333 2t + t2 = 0 + 14.33333333 Combine like terms: 0 + 14.33333333 = 14.33333333 2t + t2 = 14.33333333 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 = 14.33333333 + 1 Reorder the terms: 1 + 2t + t2 = 14.33333333 + 1 Combine like terms: 14.33333333 + 1 = 15.33333333 1 + 2t + t2 = 15.33333333 Factor a perfect square on the left side: (t + 1)(t + 1) = 15.33333333 Calculate the square root of the right side: 3.915780041 Break this problem into two subproblems by setting (t + 1) equal to 3.915780041 and -3.915780041.Subproblem 1
t + 1 = 3.915780041 Simplifying t + 1 = 3.915780041 Reorder the terms: 1 + t = 3.915780041 Solving 1 + t = 3.915780041 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 = 3.915780041 + -1 Combine like terms: 1 + -1 = 0 0 + t = 3.915780041 + -1 t = 3.915780041 + -1 Combine like terms: 3.915780041 + -1 = 2.915780041 t = 2.915780041 Simplifying t = 2.915780041Subproblem 2
t + 1 = -3.915780041 Simplifying t + 1 = -3.915780041 Reorder the terms: 1 + t = -3.915780041 Solving 1 + t = -3.915780041 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 = -3.915780041 + -1 Combine like terms: 1 + -1 = 0 0 + t = -3.915780041 + -1 t = -3.915780041 + -1 Combine like terms: -3.915780041 + -1 = -4.915780041 t = -4.915780041 Simplifying t = -4.915780041Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.915780041, -4.915780041}
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