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Simplifying 2t2 + -21t + 2 = 0 Reorder the terms: 2 + -21t + 2t2 = 0 Solving 2 + -21t + 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'. 1 + -10.5t + t2 = 0 Move the constant term to the right: Add '-1' to each side of the equation. 1 + -10.5t + -1 + t2 = 0 + -1 Reorder the terms: 1 + -1 + -10.5t + t2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -10.5t + t2 = 0 + -1 -10.5t + t2 = 0 + -1 Combine like terms: 0 + -1 = -1 -10.5t + t2 = -1 The t term is -10.5t. Take half its coefficient (-5.25). Square it (27.5625) and add it to both sides. Add '27.5625' to each side of the equation. -10.5t + 27.5625 + t2 = -1 + 27.5625 Reorder the terms: 27.5625 + -10.5t + t2 = -1 + 27.5625 Combine like terms: -1 + 27.5625 = 26.5625 27.5625 + -10.5t + t2 = 26.5625 Factor a perfect square on the left side: (t + -5.25)(t + -5.25) = 26.5625 Calculate the square root of the right side: 5.153882032 Break this problem into two subproblems by setting (t + -5.25) equal to 5.153882032 and -5.153882032.Subproblem 1
t + -5.25 = 5.153882032 Simplifying t + -5.25 = 5.153882032 Reorder the terms: -5.25 + t = 5.153882032 Solving -5.25 + t = 5.153882032 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '5.25' to each side of the equation. -5.25 + 5.25 + t = 5.153882032 + 5.25 Combine like terms: -5.25 + 5.25 = 0.00 0.00 + t = 5.153882032 + 5.25 t = 5.153882032 + 5.25 Combine like terms: 5.153882032 + 5.25 = 10.403882032 t = 10.403882032 Simplifying t = 10.403882032Subproblem 2
t + -5.25 = -5.153882032 Simplifying t + -5.25 = -5.153882032 Reorder the terms: -5.25 + t = -5.153882032 Solving -5.25 + t = -5.153882032 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '5.25' to each side of the equation. -5.25 + 5.25 + t = -5.153882032 + 5.25 Combine like terms: -5.25 + 5.25 = 0.00 0.00 + t = -5.153882032 + 5.25 t = -5.153882032 + 5.25 Combine like terms: -5.153882032 + 5.25 = 0.096117968 t = 0.096117968 Simplifying t = 0.096117968Solution
The solution to the problem is based on the solutions from the subproblems. t = {10.403882032, 0.096117968}
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