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Simplifying 0 = -4.9t2 + 29.4t + 2.5 Reorder the terms: 0 = 2.5 + 29.4t + -4.9t2 Solving 0 = 2.5 + 29.4t + -4.9t2 Solving for variable 't'. Combine like terms: 0 + -2.5 = -2.5 -2.5 + -29.4t + 4.9t2 = 2.5 + 29.4t + -4.9t2 + -2.5 + -29.4t + 4.9t2 Reorder the terms: -2.5 + -29.4t + 4.9t2 = 2.5 + -2.5 + 29.4t + -29.4t + -4.9t2 + 4.9t2 Combine like terms: 2.5 + -2.5 = 0.0 -2.5 + -29.4t + 4.9t2 = 0.0 + 29.4t + -29.4t + -4.9t2 + 4.9t2 -2.5 + -29.4t + 4.9t2 = 29.4t + -29.4t + -4.9t2 + 4.9t2 Combine like terms: 29.4t + -29.4t = 0.0 -2.5 + -29.4t + 4.9t2 = 0.0 + -4.9t2 + 4.9t2 -2.5 + -29.4t + 4.9t2 = -4.9t2 + 4.9t2 Combine like terms: -4.9t2 + 4.9t2 = 0.0 -2.5 + -29.4t + 4.9t2 = 0.0 Begin completing the square. Divide all terms by 4.9 the coefficient of the squared term: Divide each side by '4.9'. -0.5102040816 + -6t + t2 = 0 Move the constant term to the right: Add '0.5102040816' to each side of the equation. -0.5102040816 + -6t + 0.5102040816 + t2 = 0 + 0.5102040816 Reorder the terms: -0.5102040816 + 0.5102040816 + -6t + t2 = 0 + 0.5102040816 Combine like terms: -0.5102040816 + 0.5102040816 = 0.0000000000 0.0000000000 + -6t + t2 = 0 + 0.5102040816 -6t + t2 = 0 + 0.5102040816 Combine like terms: 0 + 0.5102040816 = 0.5102040816 -6t + t2 = 0.5102040816 The t term is -6t. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6t + 9 + t2 = 0.5102040816 + 9 Reorder the terms: 9 + -6t + t2 = 0.5102040816 + 9 Combine like terms: 0.5102040816 + 9 = 9.5102040816 9 + -6t + t2 = 9.5102040816 Factor a perfect square on the left side: (t + -3)(t + -3) = 9.5102040816 Calculate the square root of the right side: 3.083861878 Break this problem into two subproblems by setting (t + -3) equal to 3.083861878 and -3.083861878.Subproblem 1
t + -3 = 3.083861878 Simplifying t + -3 = 3.083861878 Reorder the terms: -3 + t = 3.083861878 Solving -3 + t = 3.083861878 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + t = 3.083861878 + 3 Combine like terms: -3 + 3 = 0 0 + t = 3.083861878 + 3 t = 3.083861878 + 3 Combine like terms: 3.083861878 + 3 = 6.083861878 t = 6.083861878 Simplifying t = 6.083861878Subproblem 2
t + -3 = -3.083861878 Simplifying t + -3 = -3.083861878 Reorder the terms: -3 + t = -3.083861878 Solving -3 + t = -3.083861878 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + t = -3.083861878 + 3 Combine like terms: -3 + 3 = 0 0 + t = -3.083861878 + 3 t = -3.083861878 + 3 Combine like terms: -3.083861878 + 3 = -0.083861878 t = -0.083861878 Simplifying t = -0.083861878Solution
The solution to the problem is based on the solutions from the subproblems. t = {6.083861878, -0.083861878}
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