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Simplifying 50 + 10t = t2 Solving 50 + 10t = t2 Solving for variable 't'. Combine like terms: t2 + -1t2 = 0 50 + 10t + -1t2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -50 + -10t + t2 = 0 Move the constant term to the right: Add '50' to each side of the equation. -50 + -10t + 50 + t2 = 0 + 50 Reorder the terms: -50 + 50 + -10t + t2 = 0 + 50 Combine like terms: -50 + 50 = 0 0 + -10t + t2 = 0 + 50 -10t + t2 = 0 + 50 Combine like terms: 0 + 50 = 50 -10t + t2 = 50 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 = 50 + 25 Reorder the terms: 25 + -10t + t2 = 50 + 25 Combine like terms: 50 + 25 = 75 25 + -10t + t2 = 75 Factor a perfect square on the left side: (t + -5)(t + -5) = 75 Calculate the square root of the right side: 8.660254038 Break this problem into two subproblems by setting (t + -5) equal to 8.660254038 and -8.660254038.Subproblem 1
t + -5 = 8.660254038 Simplifying t + -5 = 8.660254038 Reorder the terms: -5 + t = 8.660254038 Solving -5 + t = 8.660254038 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 = 8.660254038 + 5 Combine like terms: -5 + 5 = 0 0 + t = 8.660254038 + 5 t = 8.660254038 + 5 Combine like terms: 8.660254038 + 5 = 13.660254038 t = 13.660254038 Simplifying t = 13.660254038Subproblem 2
t + -5 = -8.660254038 Simplifying t + -5 = -8.660254038 Reorder the terms: -5 + t = -8.660254038 Solving -5 + t = -8.660254038 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 = -8.660254038 + 5 Combine like terms: -5 + 5 = 0 0 + t = -8.660254038 + 5 t = -8.660254038 + 5 Combine like terms: -8.660254038 + 5 = -3.660254038 t = -3.660254038 Simplifying t = -3.660254038Solution
The solution to the problem is based on the solutions from the subproblems. t = {13.660254038, -3.660254038}
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