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Simplifying -16t2 + -40t + 9 = 0 Reorder the terms: 9 + -40t + -16t2 = 0 Solving 9 + -40t + -16t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by -16 the coefficient of the squared term: Divide each side by '-16'. -0.5625 + 2.5t + t2 = 0 Move the constant term to the right: Add '0.5625' to each side of the equation. -0.5625 + 2.5t + 0.5625 + t2 = 0 + 0.5625 Reorder the terms: -0.5625 + 0.5625 + 2.5t + t2 = 0 + 0.5625 Combine like terms: -0.5625 + 0.5625 = 0.0000 0.0000 + 2.5t + t2 = 0 + 0.5625 2.5t + t2 = 0 + 0.5625 Combine like terms: 0 + 0.5625 = 0.5625 2.5t + t2 = 0.5625 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 = 0.5625 + 1.5625 Reorder the terms: 1.5625 + 2.5t + t2 = 0.5625 + 1.5625 Combine like terms: 0.5625 + 1.5625 = 2.125 1.5625 + 2.5t + t2 = 2.125 Factor a perfect square on the left side: (t + 1.25)(t + 1.25) = 2.125 Calculate the square root of the right side: 1.457737974 Break this problem into two subproblems by setting (t + 1.25) equal to 1.457737974 and -1.457737974.Subproblem 1
t + 1.25 = 1.457737974 Simplifying t + 1.25 = 1.457737974 Reorder the terms: 1.25 + t = 1.457737974 Solving 1.25 + t = 1.457737974 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 = 1.457737974 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + t = 1.457737974 + -1.25 t = 1.457737974 + -1.25 Combine like terms: 1.457737974 + -1.25 = 0.207737974 t = 0.207737974 Simplifying t = 0.207737974Subproblem 2
t + 1.25 = -1.457737974 Simplifying t + 1.25 = -1.457737974 Reorder the terms: 1.25 + t = -1.457737974 Solving 1.25 + t = -1.457737974 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 = -1.457737974 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + t = -1.457737974 + -1.25 t = -1.457737974 + -1.25 Combine like terms: -1.457737974 + -1.25 = -2.707737974 t = -2.707737974 Simplifying t = -2.707737974Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.207737974, -2.707737974}
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