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Simplifying 5t2 + 3t + -50 = 0 Reorder the terms: -50 + 3t + 5t2 = 0 Solving -50 + 3t + 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'. -10 + 0.6t + t2 = 0 Move the constant term to the right: Add '10' to each side of the equation. -10 + 0.6t + 10 + t2 = 0 + 10 Reorder the terms: -10 + 10 + 0.6t + t2 = 0 + 10 Combine like terms: -10 + 10 = 0 0 + 0.6t + t2 = 0 + 10 0.6t + t2 = 0 + 10 Combine like terms: 0 + 10 = 10 0.6t + t2 = 10 The t term is 0.6t. Take half its coefficient (0.3). Square it (0.09) and add it to both sides. Add '0.09' to each side of the equation. 0.6t + 0.09 + t2 = 10 + 0.09 Reorder the terms: 0.09 + 0.6t + t2 = 10 + 0.09 Combine like terms: 10 + 0.09 = 10.09 0.09 + 0.6t + t2 = 10.09 Factor a perfect square on the left side: (t + 0.3)(t + 0.3) = 10.09 Calculate the square root of the right side: 3.176476035 Break this problem into two subproblems by setting (t + 0.3) equal to 3.176476035 and -3.176476035.Subproblem 1
t + 0.3 = 3.176476035 Simplifying t + 0.3 = 3.176476035 Reorder the terms: 0.3 + t = 3.176476035 Solving 0.3 + t = 3.176476035 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.3' to each side of the equation. 0.3 + -0.3 + t = 3.176476035 + -0.3 Combine like terms: 0.3 + -0.3 = 0.0 0.0 + t = 3.176476035 + -0.3 t = 3.176476035 + -0.3 Combine like terms: 3.176476035 + -0.3 = 2.876476035 t = 2.876476035 Simplifying t = 2.876476035Subproblem 2
t + 0.3 = -3.176476035 Simplifying t + 0.3 = -3.176476035 Reorder the terms: 0.3 + t = -3.176476035 Solving 0.3 + t = -3.176476035 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.3' to each side of the equation. 0.3 + -0.3 + t = -3.176476035 + -0.3 Combine like terms: 0.3 + -0.3 = 0.0 0.0 + t = -3.176476035 + -0.3 t = -3.176476035 + -0.3 Combine like terms: -3.176476035 + -0.3 = -3.476476035 t = -3.476476035 Simplifying t = -3.476476035Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.876476035, -3.476476035}
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