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Simplifying 0 = 2 + 25t + -5t2 Solving 0 = 2 + 25t + -5t2 Solving for variable 't'. Combine like terms: 0 + -2 = -2 -2 + -25t + 5t2 = 2 + 25t + -5t2 + -2 + -25t + 5t2 Reorder the terms: -2 + -25t + 5t2 = 2 + -2 + 25t + -25t + -5t2 + 5t2 Combine like terms: 2 + -2 = 0 -2 + -25t + 5t2 = 0 + 25t + -25t + -5t2 + 5t2 -2 + -25t + 5t2 = 25t + -25t + -5t2 + 5t2 Combine like terms: 25t + -25t = 0 -2 + -25t + 5t2 = 0 + -5t2 + 5t2 -2 + -25t + 5t2 = -5t2 + 5t2 Combine like terms: -5t2 + 5t2 = 0 -2 + -25t + 5t2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -0.4 + -5t + t2 = 0 Move the constant term to the right: Add '0.4' to each side of the equation. -0.4 + -5t + 0.4 + t2 = 0 + 0.4 Reorder the terms: -0.4 + 0.4 + -5t + t2 = 0 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + -5t + t2 = 0 + 0.4 -5t + t2 = 0 + 0.4 Combine like terms: 0 + 0.4 = 0.4 -5t + t2 = 0.4 The t term is -5t. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5t + 6.25 + t2 = 0.4 + 6.25 Reorder the terms: 6.25 + -5t + t2 = 0.4 + 6.25 Combine like terms: 0.4 + 6.25 = 6.65 6.25 + -5t + t2 = 6.65 Factor a perfect square on the left side: (t + -2.5)(t + -2.5) = 6.65 Calculate the square root of the right side: 2.578759392 Break this problem into two subproblems by setting (t + -2.5) equal to 2.578759392 and -2.578759392.Subproblem 1
t + -2.5 = 2.578759392 Simplifying t + -2.5 = 2.578759392 Reorder the terms: -2.5 + t = 2.578759392 Solving -2.5 + t = 2.578759392 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + t = 2.578759392 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + t = 2.578759392 + 2.5 t = 2.578759392 + 2.5 Combine like terms: 2.578759392 + 2.5 = 5.078759392 t = 5.078759392 Simplifying t = 5.078759392Subproblem 2
t + -2.5 = -2.578759392 Simplifying t + -2.5 = -2.578759392 Reorder the terms: -2.5 + t = -2.578759392 Solving -2.5 + t = -2.578759392 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + t = -2.578759392 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + t = -2.578759392 + 2.5 t = -2.578759392 + 2.5 Combine like terms: -2.578759392 + 2.5 = -0.078759392 t = -0.078759392 Simplifying t = -0.078759392Solution
The solution to the problem is based on the solutions from the subproblems. t = {5.078759392, -0.078759392}
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