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Simplifying 2t2 + 5t + -63 = 63 Reorder the terms: -63 + 5t + 2t2 = 63 Solving -63 + 5t + 2t2 = 63 Solving for variable 't'. Reorder the terms: -63 + -63 + 5t + 2t2 = 63 + -63 Combine like terms: -63 + -63 = -126 -126 + 5t + 2t2 = 63 + -63 Combine like terms: 63 + -63 = 0 -126 + 5t + 2t2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -63 + 2.5t + t2 = 0 Move the constant term to the right: Add '63' to each side of the equation. -63 + 2.5t + 63 + t2 = 0 + 63 Reorder the terms: -63 + 63 + 2.5t + t2 = 0 + 63 Combine like terms: -63 + 63 = 0 0 + 2.5t + t2 = 0 + 63 2.5t + t2 = 0 + 63 Combine like terms: 0 + 63 = 63 2.5t + t2 = 63 The t term is 2.5t. Take half its coefficient (1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. 2.5t + 1.5625 + t2 = 63 + 1.5625 Reorder the terms: 1.5625 + 2.5t + t2 = 63 + 1.5625 Combine like terms: 63 + 1.5625 = 64.5625 1.5625 + 2.5t + t2 = 64.5625 Factor a perfect square on the left side: (t + 1.25)(t + 1.25) = 64.5625 Calculate the square root of the right side: 8.03507934 Break this problem into two subproblems by setting (t + 1.25) equal to 8.03507934 and -8.03507934.Subproblem 1
t + 1.25 = 8.03507934 Simplifying t + 1.25 = 8.03507934 Reorder the terms: 1.25 + t = 8.03507934 Solving 1.25 + t = 8.03507934 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + t = 8.03507934 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + t = 8.03507934 + -1.25 t = 8.03507934 + -1.25 Combine like terms: 8.03507934 + -1.25 = 6.78507934 t = 6.78507934 Simplifying t = 6.78507934Subproblem 2
t + 1.25 = -8.03507934 Simplifying t + 1.25 = -8.03507934 Reorder the terms: 1.25 + t = -8.03507934 Solving 1.25 + t = -8.03507934 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + t = -8.03507934 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + t = -8.03507934 + -1.25 t = -8.03507934 + -1.25 Combine like terms: -8.03507934 + -1.25 = -9.28507934 t = -9.28507934 Simplifying t = -9.28507934Solution
The solution to the problem is based on the solutions from the subproblems. t = {6.78507934, -9.28507934}
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