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Simplifying 8t2 + 20t + -9 = 0 Reorder the terms: -9 + 20t + 8t2 = 0 Solving -9 + 20t + 8t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -1.125 + 2.5t + t2 = 0 Move the constant term to the right: Add '1.125' to each side of the equation. -1.125 + 2.5t + 1.125 + t2 = 0 + 1.125 Reorder the terms: -1.125 + 1.125 + 2.5t + t2 = 0 + 1.125 Combine like terms: -1.125 + 1.125 = 0.000 0.000 + 2.5t + t2 = 0 + 1.125 2.5t + t2 = 0 + 1.125 Combine like terms: 0 + 1.125 = 1.125 2.5t + t2 = 1.125 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 = 1.125 + 1.5625 Reorder the terms: 1.5625 + 2.5t + t2 = 1.125 + 1.5625 Combine like terms: 1.125 + 1.5625 = 2.6875 1.5625 + 2.5t + t2 = 2.6875 Factor a perfect square on the left side: (t + 1.25)(t + 1.25) = 2.6875 Calculate the square root of the right side: 1.639359631 Break this problem into two subproblems by setting (t + 1.25) equal to 1.639359631 and -1.639359631.Subproblem 1
t + 1.25 = 1.639359631 Simplifying t + 1.25 = 1.639359631 Reorder the terms: 1.25 + t = 1.639359631 Solving 1.25 + t = 1.639359631 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 = 1.639359631 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + t = 1.639359631 + -1.25 t = 1.639359631 + -1.25 Combine like terms: 1.639359631 + -1.25 = 0.389359631 t = 0.389359631 Simplifying t = 0.389359631Subproblem 2
t + 1.25 = -1.639359631 Simplifying t + 1.25 = -1.639359631 Reorder the terms: 1.25 + t = -1.639359631 Solving 1.25 + t = -1.639359631 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 = -1.639359631 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + t = -1.639359631 + -1.25 t = -1.639359631 + -1.25 Combine like terms: -1.639359631 + -1.25 = -2.889359631 t = -2.889359631 Simplifying t = -2.889359631Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.389359631, -2.889359631}
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