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Simplifying 5t2 + -1t + -5 = 0 Reorder the terms: -5 + -1t + 5t2 = 0 Solving -5 + -1t + 5t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -1 + -0.2t + t2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + -0.2t + 1 + t2 = 0 + 1 Reorder the terms: -1 + 1 + -0.2t + t2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -0.2t + t2 = 0 + 1 -0.2t + t2 = 0 + 1 Combine like terms: 0 + 1 = 1 -0.2t + t2 = 1 The t term is -0.2t. Take half its coefficient (-0.1). Square it (0.01) and add it to both sides. Add '0.01' to each side of the equation. -0.2t + 0.01 + t2 = 1 + 0.01 Reorder the terms: 0.01 + -0.2t + t2 = 1 + 0.01 Combine like terms: 1 + 0.01 = 1.01 0.01 + -0.2t + t2 = 1.01 Factor a perfect square on the left side: (t + -0.1)(t + -0.1) = 1.01 Calculate the square root of the right side: 1.004987562 Break this problem into two subproblems by setting (t + -0.1) equal to 1.004987562 and -1.004987562.Subproblem 1
t + -0.1 = 1.004987562 Simplifying t + -0.1 = 1.004987562 Reorder the terms: -0.1 + t = 1.004987562 Solving -0.1 + t = 1.004987562 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.1' to each side of the equation. -0.1 + 0.1 + t = 1.004987562 + 0.1 Combine like terms: -0.1 + 0.1 = 0.0 0.0 + t = 1.004987562 + 0.1 t = 1.004987562 + 0.1 Combine like terms: 1.004987562 + 0.1 = 1.104987562 t = 1.104987562 Simplifying t = 1.104987562Subproblem 2
t + -0.1 = -1.004987562 Simplifying t + -0.1 = -1.004987562 Reorder the terms: -0.1 + t = -1.004987562 Solving -0.1 + t = -1.004987562 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.1' to each side of the equation. -0.1 + 0.1 + t = -1.004987562 + 0.1 Combine like terms: -0.1 + 0.1 = 0.0 0.0 + t = -1.004987562 + 0.1 t = -1.004987562 + 0.1 Combine like terms: -1.004987562 + 0.1 = -0.904987562 t = -0.904987562 Simplifying t = -0.904987562Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.104987562, -0.904987562}
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