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Simplifying -16t2 + t + 25 = 0 Reorder the terms: 25 + t + -16t2 = 0 Solving 25 + t + -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'. -1.5625 + -0.0625t + t2 = 0 Move the constant term to the right: Add '1.5625' to each side of the equation. -1.5625 + -0.0625t + 1.5625 + t2 = 0 + 1.5625 Reorder the terms: -1.5625 + 1.5625 + -0.0625t + t2 = 0 + 1.5625 Combine like terms: -1.5625 + 1.5625 = 0.0000 0.0000 + -0.0625t + t2 = 0 + 1.5625 -0.0625t + t2 = 0 + 1.5625 Combine like terms: 0 + 1.5625 = 1.5625 -0.0625t + t2 = 1.5625 The t term is t. 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. -0.0625t + 0.25 + t2 = 1.5625 + 0.25 Reorder the terms: 0.25 + -0.0625t + t2 = 1.5625 + 0.25 Combine like terms: 1.5625 + 0.25 = 1.8125 0.25 + -0.0625t + 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 = 0.846291202 t = 0.846291202 Simplifying t = 0.846291202Subproblem 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 = -1.846291202 t = -1.846291202 Simplifying t = -1.846291202Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.846291202, -1.846291202}
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