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Simplifying 10 = t2 + 50t Reorder the terms: 10 = 50t + t2 Solving 10 = 50t + t2 Solving for variable 't'. Reorder the terms: 10 + -50t + -1t2 = 50t + -50t + t2 + -1t2 Combine like terms: 50t + -50t = 0 10 + -50t + -1t2 = 0 + t2 + -1t2 10 + -50t + -1t2 = t2 + -1t2 Combine like terms: t2 + -1t2 = 0 10 + -50t + -1t2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -10 + 50t + t2 = 0 Move the constant term to the right: Add '10' to each side of the equation. -10 + 50t + 10 + t2 = 0 + 10 Reorder the terms: -10 + 10 + 50t + t2 = 0 + 10 Combine like terms: -10 + 10 = 0 0 + 50t + t2 = 0 + 10 50t + t2 = 0 + 10 Combine like terms: 0 + 10 = 10 50t + t2 = 10 The t term is 50t. Take half its coefficient (25). Square it (625) and add it to both sides. Add '625' to each side of the equation. 50t + 625 + t2 = 10 + 625 Reorder the terms: 625 + 50t + t2 = 10 + 625 Combine like terms: 10 + 625 = 635 625 + 50t + t2 = 635 Factor a perfect square on the left side: (t + 25)(t + 25) = 635 Calculate the square root of the right side: 25.199206337 Break this problem into two subproblems by setting (t + 25) equal to 25.199206337 and -25.199206337.Subproblem 1
t + 25 = 25.199206337 Simplifying t + 25 = 25.199206337 Reorder the terms: 25 + t = 25.199206337 Solving 25 + t = 25.199206337 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-25' to each side of the equation. 25 + -25 + t = 25.199206337 + -25 Combine like terms: 25 + -25 = 0 0 + t = 25.199206337 + -25 t = 25.199206337 + -25 Combine like terms: 25.199206337 + -25 = 0.199206337 t = 0.199206337 Simplifying t = 0.199206337Subproblem 2
t + 25 = -25.199206337 Simplifying t + 25 = -25.199206337 Reorder the terms: 25 + t = -25.199206337 Solving 25 + t = -25.199206337 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-25' to each side of the equation. 25 + -25 + t = -25.199206337 + -25 Combine like terms: 25 + -25 = 0 0 + t = -25.199206337 + -25 t = -25.199206337 + -25 Combine like terms: -25.199206337 + -25 = -50.199206337 t = -50.199206337 Simplifying t = -50.199206337Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.199206337, -50.199206337}
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