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Simplifying -4.9t2 + 24.5t + 8.8 = 0 Reorder the terms: 8.8 + 24.5t + -4.9t2 = 0 Solving 8.8 + 24.5t + -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'. -1.795918367 + -5t + t2 = 0 Move the constant term to the right: Add '1.795918367' to each side of the equation. -1.795918367 + -5t + 1.795918367 + t2 = 0 + 1.795918367 Reorder the terms: -1.795918367 + 1.795918367 + -5t + t2 = 0 + 1.795918367 Combine like terms: -1.795918367 + 1.795918367 = 0.000000000 0.000000000 + -5t + t2 = 0 + 1.795918367 -5t + t2 = 0 + 1.795918367 Combine like terms: 0 + 1.795918367 = 1.795918367 -5t + t2 = 1.795918367 The t term is -5t. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5t + 6.25 + t2 = 1.795918367 + 6.25 Reorder the terms: 6.25 + -5t + t2 = 1.795918367 + 6.25 Combine like terms: 1.795918367 + 6.25 = 8.045918367 6.25 + -5t + t2 = 8.045918367 Factor a perfect square on the left side: (t + -2.5)(t + -2.5) = 8.045918367 Calculate the square root of the right side: 2.836532807 Break this problem into two subproblems by setting (t + -2.5) equal to 2.836532807 and -2.836532807.Subproblem 1
t + -2.5 = 2.836532807 Simplifying t + -2.5 = 2.836532807 Reorder the terms: -2.5 + t = 2.836532807 Solving -2.5 + t = 2.836532807 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + t = 2.836532807 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + t = 2.836532807 + 2.5 t = 2.836532807 + 2.5 Combine like terms: 2.836532807 + 2.5 = 5.336532807 t = 5.336532807 Simplifying t = 5.336532807Subproblem 2
t + -2.5 = -2.836532807 Simplifying t + -2.5 = -2.836532807 Reorder the terms: -2.5 + t = -2.836532807 Solving -2.5 + t = -2.836532807 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + t = -2.836532807 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + t = -2.836532807 + 2.5 t = -2.836532807 + 2.5 Combine like terms: -2.836532807 + 2.5 = -0.336532807 t = -0.336532807 Simplifying t = -0.336532807Solution
The solution to the problem is based on the solutions from the subproblems. t = {5.336532807, -0.336532807}
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