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Simplifying 2t2 + -9t + -21 = 0 Reorder the terms: -21 + -9t + 2t2 = 0 Solving -21 + -9t + 2t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -10.5 + -4.5t + t2 = 0 Move the constant term to the right: Add '10.5' to each side of the equation. -10.5 + -4.5t + 10.5 + t2 = 0 + 10.5 Reorder the terms: -10.5 + 10.5 + -4.5t + t2 = 0 + 10.5 Combine like terms: -10.5 + 10.5 = 0.0 0.0 + -4.5t + t2 = 0 + 10.5 -4.5t + t2 = 0 + 10.5 Combine like terms: 0 + 10.5 = 10.5 -4.5t + t2 = 10.5 The t term is -4.5t. Take half its coefficient (-2.25). Square it (5.0625) and add it to both sides. Add '5.0625' to each side of the equation. -4.5t + 5.0625 + t2 = 10.5 + 5.0625 Reorder the terms: 5.0625 + -4.5t + t2 = 10.5 + 5.0625 Combine like terms: 10.5 + 5.0625 = 15.5625 5.0625 + -4.5t + t2 = 15.5625 Factor a perfect square on the left side: (t + -2.25)(t + -2.25) = 15.5625 Calculate the square root of the right side: 3.94493346 Break this problem into two subproblems by setting (t + -2.25) equal to 3.94493346 and -3.94493346.Subproblem 1
t + -2.25 = 3.94493346 Simplifying t + -2.25 = 3.94493346 Reorder the terms: -2.25 + t = 3.94493346 Solving -2.25 + t = 3.94493346 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.25' to each side of the equation. -2.25 + 2.25 + t = 3.94493346 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + t = 3.94493346 + 2.25 t = 3.94493346 + 2.25 Combine like terms: 3.94493346 + 2.25 = 6.19493346 t = 6.19493346 Simplifying t = 6.19493346Subproblem 2
t + -2.25 = -3.94493346 Simplifying t + -2.25 = -3.94493346 Reorder the terms: -2.25 + t = -3.94493346 Solving -2.25 + t = -3.94493346 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.25' to each side of the equation. -2.25 + 2.25 + t = -3.94493346 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + t = -3.94493346 + 2.25 t = -3.94493346 + 2.25 Combine like terms: -3.94493346 + 2.25 = -1.69493346 t = -1.69493346 Simplifying t = -1.69493346Solution
The solution to the problem is based on the solutions from the subproblems. t = {6.19493346, -1.69493346}
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