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Simplifying 2t2 + 8t + -21 = 0 Reorder the terms: -21 + 8t + 2t2 = 0 Solving -21 + 8t + 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 + 4t + t2 = 0 Move the constant term to the right: Add '10.5' to each side of the equation. -10.5 + 4t + 10.5 + t2 = 0 + 10.5 Reorder the terms: -10.5 + 10.5 + 4t + t2 = 0 + 10.5 Combine like terms: -10.5 + 10.5 = 0.0 0.0 + 4t + t2 = 0 + 10.5 4t + t2 = 0 + 10.5 Combine like terms: 0 + 10.5 = 10.5 4t + t2 = 10.5 The t term is 4t. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4t + 4 + t2 = 10.5 + 4 Reorder the terms: 4 + 4t + t2 = 10.5 + 4 Combine like terms: 10.5 + 4 = 14.5 4 + 4t + t2 = 14.5 Factor a perfect square on the left side: (t + 2)(t + 2) = 14.5 Calculate the square root of the right side: 3.807886553 Break this problem into two subproblems by setting (t + 2) equal to 3.807886553 and -3.807886553.Subproblem 1
t + 2 = 3.807886553 Simplifying t + 2 = 3.807886553 Reorder the terms: 2 + t = 3.807886553 Solving 2 + t = 3.807886553 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + t = 3.807886553 + -2 Combine like terms: 2 + -2 = 0 0 + t = 3.807886553 + -2 t = 3.807886553 + -2 Combine like terms: 3.807886553 + -2 = 1.807886553 t = 1.807886553 Simplifying t = 1.807886553Subproblem 2
t + 2 = -3.807886553 Simplifying t + 2 = -3.807886553 Reorder the terms: 2 + t = -3.807886553 Solving 2 + t = -3.807886553 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + t = -3.807886553 + -2 Combine like terms: 2 + -2 = 0 0 + t = -3.807886553 + -2 t = -3.807886553 + -2 Combine like terms: -3.807886553 + -2 = -5.807886553 t = -5.807886553 Simplifying t = -5.807886553Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.807886553, -5.807886553}
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