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Simplifying t(3t + -7) = 3 Reorder the terms: t(-7 + 3t) = 3 (-7 * t + 3t * t) = 3 (-7t + 3t2) = 3 Solving -7t + 3t2 = 3 Solving for variable 't'. Reorder the terms: -3 + -7t + 3t2 = 3 + -3 Combine like terms: 3 + -3 = 0 -3 + -7t + 3t2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -1 + -2.333333333t + t2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + -2.333333333t + 1 + t2 = 0 + 1 Reorder the terms: -1 + 1 + -2.333333333t + t2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -2.333333333t + t2 = 0 + 1 -2.333333333t + t2 = 0 + 1 Combine like terms: 0 + 1 = 1 -2.333333333t + t2 = 1 The t term is -2.333333333t. Take half its coefficient (-1.166666667). Square it (1.361111112) and add it to both sides. Add '1.361111112' to each side of the equation. -2.333333333t + 1.361111112 + t2 = 1 + 1.361111112 Reorder the terms: 1.361111112 + -2.333333333t + t2 = 1 + 1.361111112 Combine like terms: 1 + 1.361111112 = 2.361111112 1.361111112 + -2.333333333t + t2 = 2.361111112 Factor a perfect square on the left side: (t + -1.166666667)(t + -1.166666667) = 2.361111112 Calculate the square root of the right side: 1.536590743 Break this problem into two subproblems by setting (t + -1.166666667) equal to 1.536590743 and -1.536590743.Subproblem 1
t + -1.166666667 = 1.536590743 Simplifying t + -1.166666667 = 1.536590743 Reorder the terms: -1.166666667 + t = 1.536590743 Solving -1.166666667 + t = 1.536590743 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.166666667' to each side of the equation. -1.166666667 + 1.166666667 + t = 1.536590743 + 1.166666667 Combine like terms: -1.166666667 + 1.166666667 = 0.000000000 0.000000000 + t = 1.536590743 + 1.166666667 t = 1.536590743 + 1.166666667 Combine like terms: 1.536590743 + 1.166666667 = 2.70325741 t = 2.70325741 Simplifying t = 2.70325741Subproblem 2
t + -1.166666667 = -1.536590743 Simplifying t + -1.166666667 = -1.536590743 Reorder the terms: -1.166666667 + t = -1.536590743 Solving -1.166666667 + t = -1.536590743 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.166666667' to each side of the equation. -1.166666667 + 1.166666667 + t = -1.536590743 + 1.166666667 Combine like terms: -1.166666667 + 1.166666667 = 0.000000000 0.000000000 + t = -1.536590743 + 1.166666667 t = -1.536590743 + 1.166666667 Combine like terms: -1.536590743 + 1.166666667 = -0.369924076 t = -0.369924076 Simplifying t = -0.369924076Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.70325741, -0.369924076}
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