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Simplifying -4.9t2 + 34.3t + 1.5 = 0 Reorder the terms: 1.5 + 34.3t + -4.9t2 = 0 Solving 1.5 + 34.3t + -4.9t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by -4.9 the coefficient of the squared term: Divide each side by '-4.9'. -0.306122449 + -7t + t2 = 0 Move the constant term to the right: Add '0.306122449' to each side of the equation. -0.306122449 + -7t + 0.306122449 + t2 = 0 + 0.306122449 Reorder the terms: -0.306122449 + 0.306122449 + -7t + t2 = 0 + 0.306122449 Combine like terms: -0.306122449 + 0.306122449 = 0.000000000 0.000000000 + -7t + t2 = 0 + 0.306122449 -7t + t2 = 0 + 0.306122449 Combine like terms: 0 + 0.306122449 = 0.306122449 -7t + t2 = 0.306122449 The t term is -7t. Take half its coefficient (-3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. -7t + 12.25 + t2 = 0.306122449 + 12.25 Reorder the terms: 12.25 + -7t + t2 = 0.306122449 + 12.25 Combine like terms: 0.306122449 + 12.25 = 12.556122449 12.25 + -7t + t2 = 12.556122449 Factor a perfect square on the left side: (t + -3.5)(t + -3.5) = 12.556122449 Calculate the square root of the right side: 3.54346193 Break this problem into two subproblems by setting (t + -3.5) equal to 3.54346193 and -3.54346193.Subproblem 1
t + -3.5 = 3.54346193 Simplifying t + -3.5 = 3.54346193 Reorder the terms: -3.5 + t = 3.54346193 Solving -3.5 + t = 3.54346193 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + t = 3.54346193 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + t = 3.54346193 + 3.5 t = 3.54346193 + 3.5 Combine like terms: 3.54346193 + 3.5 = 7.04346193 t = 7.04346193 Simplifying t = 7.04346193Subproblem 2
t + -3.5 = -3.54346193 Simplifying t + -3.5 = -3.54346193 Reorder the terms: -3.5 + t = -3.54346193 Solving -3.5 + t = -3.54346193 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + t = -3.54346193 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + t = -3.54346193 + 3.5 t = -3.54346193 + 3.5 Combine like terms: -3.54346193 + 3.5 = -0.04346193 t = -0.04346193 Simplifying t = -0.04346193Solution
The solution to the problem is based on the solutions from the subproblems. t = {7.04346193, -0.04346193}
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