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Simplifying 0 = -16t2 + 16t + 25 Reorder the terms: 0 = 25 + 16t + -16t2 Solving 0 = 25 + 16t + -16t2 Solving for variable 't'. Combine like terms: 0 + -25 = -25 -25 + -16t + 16t2 = 25 + 16t + -16t2 + -25 + -16t + 16t2 Reorder the terms: -25 + -16t + 16t2 = 25 + -25 + 16t + -16t + -16t2 + 16t2 Combine like terms: 25 + -25 = 0 -25 + -16t + 16t2 = 0 + 16t + -16t + -16t2 + 16t2 -25 + -16t + 16t2 = 16t + -16t + -16t2 + 16t2 Combine like terms: 16t + -16t = 0 -25 + -16t + 16t2 = 0 + -16t2 + 16t2 -25 + -16t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -25 + -16t + 16t2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -1.5625 + -1t + t2 = 0 Move the constant term to the right: Add '1.5625' to each side of the equation. -1.5625 + -1t + 1.5625 + t2 = 0 + 1.5625 Reorder the terms: -1.5625 + 1.5625 + -1t + t2 = 0 + 1.5625 Combine like terms: -1.5625 + 1.5625 = 0.0000 0.0000 + -1t + t2 = 0 + 1.5625 -1t + t2 = 0 + 1.5625 Combine like terms: 0 + 1.5625 = 1.5625 -1t + t2 = 1.5625 The t term is -1t. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1t + 0.25 + t2 = 1.5625 + 0.25 Reorder the terms: 0.25 + -1t + t2 = 1.5625 + 0.25 Combine like terms: 1.5625 + 0.25 = 1.8125 0.25 + -1t + t2 = 1.8125 Factor a perfect square on the left side: (t + -0.5)(t + -0.5) = 1.8125 Calculate the square root of the right side: 1.346291202 Break this problem into two subproblems by setting (t + -0.5) equal to 1.346291202 and -1.346291202.Subproblem 1
t + -0.5 = 1.346291202 Simplifying t + -0.5 = 1.346291202 Reorder the terms: -0.5 + t = 1.346291202 Solving -0.5 + t = 1.346291202 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + t = 1.346291202 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + t = 1.346291202 + 0.5 t = 1.346291202 + 0.5 Combine like terms: 1.346291202 + 0.5 = 1.846291202 t = 1.846291202 Simplifying t = 1.846291202Subproblem 2
t + -0.5 = -1.346291202 Simplifying t + -0.5 = -1.346291202 Reorder the terms: -0.5 + t = -1.346291202 Solving -0.5 + t = -1.346291202 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + t = -1.346291202 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + t = -1.346291202 + 0.5 t = -1.346291202 + 0.5 Combine like terms: -1.346291202 + 0.5 = -0.846291202 t = -0.846291202 Simplifying t = -0.846291202Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.846291202, -0.846291202}
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