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Simplifying 50 = t2 + -20t Reorder the terms: 50 = -20t + t2 Solving 50 = -20t + t2 Solving for variable 't'. Reorder the terms: 50 + 20t + -1t2 = -20t + 20t + t2 + -1t2 Combine like terms: -20t + 20t = 0 50 + 20t + -1t2 = 0 + t2 + -1t2 50 + 20t + -1t2 = t2 + -1t2 Combine like terms: t2 + -1t2 = 0 50 + 20t + -1t2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -50 + -20t + t2 = 0 Move the constant term to the right: Add '50' to each side of the equation. -50 + -20t + 50 + t2 = 0 + 50 Reorder the terms: -50 + 50 + -20t + t2 = 0 + 50 Combine like terms: -50 + 50 = 0 0 + -20t + t2 = 0 + 50 -20t + t2 = 0 + 50 Combine like terms: 0 + 50 = 50 -20t + t2 = 50 The t term is -20t. Take half its coefficient (-10). Square it (100) and add it to both sides. Add '100' to each side of the equation. -20t + 100 + t2 = 50 + 100 Reorder the terms: 100 + -20t + t2 = 50 + 100 Combine like terms: 50 + 100 = 150 100 + -20t + t2 = 150 Factor a perfect square on the left side: (t + -10)(t + -10) = 150 Calculate the square root of the right side: 12.247448714 Break this problem into two subproblems by setting (t + -10) equal to 12.247448714 and -12.247448714.Subproblem 1
t + -10 = 12.247448714 Simplifying t + -10 = 12.247448714 Reorder the terms: -10 + t = 12.247448714 Solving -10 + t = 12.247448714 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + t = 12.247448714 + 10 Combine like terms: -10 + 10 = 0 0 + t = 12.247448714 + 10 t = 12.247448714 + 10 Combine like terms: 12.247448714 + 10 = 22.247448714 t = 22.247448714 Simplifying t = 22.247448714Subproblem 2
t + -10 = -12.247448714 Simplifying t + -10 = -12.247448714 Reorder the terms: -10 + t = -12.247448714 Solving -10 + t = -12.247448714 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + t = -12.247448714 + 10 Combine like terms: -10 + 10 = 0 0 + t = -12.247448714 + 10 t = -12.247448714 + 10 Combine like terms: -12.247448714 + 10 = -2.247448714 t = -2.247448714 Simplifying t = -2.247448714Solution
The solution to the problem is based on the solutions from the subproblems. t = {22.247448714, -2.247448714}
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