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Simplifying 0 = -5t2 + 50t + 2 Reorder the terms: 0 = 2 + 50t + -5t2 Solving 0 = 2 + 50t + -5t2 Solving for variable 't'. Combine like terms: 0 + -2 = -2 -2 + -50t + 5t2 = 2 + 50t + -5t2 + -2 + -50t + 5t2 Reorder the terms: -2 + -50t + 5t2 = 2 + -2 + 50t + -50t + -5t2 + 5t2 Combine like terms: 2 + -2 = 0 -2 + -50t + 5t2 = 0 + 50t + -50t + -5t2 + 5t2 -2 + -50t + 5t2 = 50t + -50t + -5t2 + 5t2 Combine like terms: 50t + -50t = 0 -2 + -50t + 5t2 = 0 + -5t2 + 5t2 -2 + -50t + 5t2 = -5t2 + 5t2 Combine like terms: -5t2 + 5t2 = 0 -2 + -50t + 5t2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -0.4 + -10t + t2 = 0 Move the constant term to the right: Add '0.4' to each side of the equation. -0.4 + -10t + 0.4 + t2 = 0 + 0.4 Reorder the terms: -0.4 + 0.4 + -10t + t2 = 0 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + -10t + t2 = 0 + 0.4 -10t + t2 = 0 + 0.4 Combine like terms: 0 + 0.4 = 0.4 -10t + t2 = 0.4 The t term is -10t. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10t + 25 + t2 = 0.4 + 25 Reorder the terms: 25 + -10t + t2 = 0.4 + 25 Combine like terms: 0.4 + 25 = 25.4 25 + -10t + t2 = 25.4 Factor a perfect square on the left side: (t + -5)(t + -5) = 25.4 Calculate the square root of the right side: 5.039841267 Break this problem into two subproblems by setting (t + -5) equal to 5.039841267 and -5.039841267.Subproblem 1
t + -5 = 5.039841267 Simplifying t + -5 = 5.039841267 Reorder the terms: -5 + t = 5.039841267 Solving -5 + t = 5.039841267 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + t = 5.039841267 + 5 Combine like terms: -5 + 5 = 0 0 + t = 5.039841267 + 5 t = 5.039841267 + 5 Combine like terms: 5.039841267 + 5 = 10.039841267 t = 10.039841267 Simplifying t = 10.039841267Subproblem 2
t + -5 = -5.039841267 Simplifying t + -5 = -5.039841267 Reorder the terms: -5 + t = -5.039841267 Solving -5 + t = -5.039841267 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + t = -5.039841267 + 5 Combine like terms: -5 + 5 = 0 0 + t = -5.039841267 + 5 t = -5.039841267 + 5 Combine like terms: -5.039841267 + 5 = -0.039841267 t = -0.039841267 Simplifying t = -0.039841267Solution
The solution to the problem is based on the solutions from the subproblems. t = {10.039841267, -0.039841267}
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