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Simplifying -3t2 + 21t + 2 = 0 Reorder the terms: 2 + 21t + -3t2 = 0 Solving 2 + 21t + -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'. -0.6666666667 + -7t + t2 = 0 Move the constant term to the right: Add '0.6666666667' to each side of the equation. -0.6666666667 + -7t + 0.6666666667 + t2 = 0 + 0.6666666667 Reorder the terms: -0.6666666667 + 0.6666666667 + -7t + t2 = 0 + 0.6666666667 Combine like terms: -0.6666666667 + 0.6666666667 = 0.0000000000 0.0000000000 + -7t + t2 = 0 + 0.6666666667 -7t + t2 = 0 + 0.6666666667 Combine like terms: 0 + 0.6666666667 = 0.6666666667 -7t + t2 = 0.6666666667 The t term is -7t. Take half its coefficient (-3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. -7t + 12.25 + t2 = 0.6666666667 + 12.25 Reorder the terms: 12.25 + -7t + t2 = 0.6666666667 + 12.25 Combine like terms: 0.6666666667 + 12.25 = 12.9166666667 12.25 + -7t + t2 = 12.9166666667 Factor a perfect square on the left side: (t + -3.5)(t + -3.5) = 12.9166666667 Calculate the square root of the right side: 3.593976442 Break this problem into two subproblems by setting (t + -3.5) equal to 3.593976442 and -3.593976442.Subproblem 1
t + -3.5 = 3.593976442 Simplifying t + -3.5 = 3.593976442 Reorder the terms: -3.5 + t = 3.593976442 Solving -3.5 + t = 3.593976442 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + t = 3.593976442 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + t = 3.593976442 + 3.5 t = 3.593976442 + 3.5 Combine like terms: 3.593976442 + 3.5 = 7.093976442 t = 7.093976442 Simplifying t = 7.093976442Subproblem 2
t + -3.5 = -3.593976442 Simplifying t + -3.5 = -3.593976442 Reorder the terms: -3.5 + t = -3.593976442 Solving -3.5 + t = -3.593976442 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + t = -3.593976442 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + t = -3.593976442 + 3.5 t = -3.593976442 + 3.5 Combine like terms: -3.593976442 + 3.5 = -0.093976442 t = -0.093976442 Simplifying t = -0.093976442Solution
The solution to the problem is based on the solutions from the subproblems. t = {7.093976442, -0.093976442}
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