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Simplifying 5t2 + 10.39t + -10 = 0 Reorder the terms: -10 + 10.39t + 5t2 = 0 Solving -10 + 10.39t + 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'. -2 + 2.078t + t2 = 0 Move the constant term to the right: Add '2' to each side of the equation. -2 + 2.078t + 2 + t2 = 0 + 2 Reorder the terms: -2 + 2 + 2.078t + t2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + 2.078t + t2 = 0 + 2 2.078t + t2 = 0 + 2 Combine like terms: 0 + 2 = 2 2.078t + t2 = 2 The t term is 2.078t. Take half its coefficient (1.039). Square it (1.079521) and add it to both sides. Add '1.079521' to each side of the equation. 2.078t + 1.079521 + t2 = 2 + 1.079521 Reorder the terms: 1.079521 + 2.078t + t2 = 2 + 1.079521 Combine like terms: 2 + 1.079521 = 3.079521 1.079521 + 2.078t + t2 = 3.079521 Factor a perfect square on the left side: (t + 1.039)(t + 1.039) = 3.079521 Calculate the square root of the right side: 1.754856404 Break this problem into two subproblems by setting (t + 1.039) equal to 1.754856404 and -1.754856404.Subproblem 1
t + 1.039 = 1.754856404 Simplifying t + 1.039 = 1.754856404 Reorder the terms: 1.039 + t = 1.754856404 Solving 1.039 + t = 1.754856404 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-1.039' to each side of the equation. 1.039 + -1.039 + t = 1.754856404 + -1.039 Combine like terms: 1.039 + -1.039 = 0.000 0.000 + t = 1.754856404 + -1.039 t = 1.754856404 + -1.039 Combine like terms: 1.754856404 + -1.039 = 0.715856404 t = 0.715856404 Simplifying t = 0.715856404Subproblem 2
t + 1.039 = -1.754856404 Simplifying t + 1.039 = -1.754856404 Reorder the terms: 1.039 + t = -1.754856404 Solving 1.039 + t = -1.754856404 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-1.039' to each side of the equation. 1.039 + -1.039 + t = -1.754856404 + -1.039 Combine like terms: 1.039 + -1.039 = 0.000 0.000 + t = -1.754856404 + -1.039 t = -1.754856404 + -1.039 Combine like terms: -1.754856404 + -1.039 = -2.793856404 t = -2.793856404 Simplifying t = -2.793856404Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.715856404, -2.793856404}
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