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Simplifying -4.9t2 + 14t + 300 = 0 Reorder the terms: 300 + 14t + -4.9t2 = 0 Solving 300 + 14t + -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'. -61.2244898 + -2.857142857t + t2 = 0 Move the constant term to the right: Add '61.2244898' to each side of the equation. -61.2244898 + -2.857142857t + 61.2244898 + t2 = 0 + 61.2244898 Reorder the terms: -61.2244898 + 61.2244898 + -2.857142857t + t2 = 0 + 61.2244898 Combine like terms: -61.2244898 + 61.2244898 = 0.0000000 0.0000000 + -2.857142857t + t2 = 0 + 61.2244898 -2.857142857t + t2 = 0 + 61.2244898 Combine like terms: 0 + 61.2244898 = 61.2244898 -2.857142857t + t2 = 61.2244898 The t term is -2.857142857t. Take half its coefficient (-1.428571429). Square it (2.040816328) and add it to both sides. Add '2.040816328' to each side of the equation. -2.857142857t + 2.040816328 + t2 = 61.2244898 + 2.040816328 Reorder the terms: 2.040816328 + -2.857142857t + t2 = 61.2244898 + 2.040816328 Combine like terms: 61.2244898 + 2.040816328 = 63.265306128 2.040816328 + -2.857142857t + t2 = 63.265306128 Factor a perfect square on the left side: (t + -1.428571429)(t + -1.428571429) = 63.265306128 Calculate the square root of the right side: 7.95394909 Break this problem into two subproblems by setting (t + -1.428571429) equal to 7.95394909 and -7.95394909.Subproblem 1
t + -1.428571429 = 7.95394909 Simplifying t + -1.428571429 = 7.95394909 Reorder the terms: -1.428571429 + t = 7.95394909 Solving -1.428571429 + t = 7.95394909 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.428571429' to each side of the equation. -1.428571429 + 1.428571429 + t = 7.95394909 + 1.428571429 Combine like terms: -1.428571429 + 1.428571429 = 0.000000000 0.000000000 + t = 7.95394909 + 1.428571429 t = 7.95394909 + 1.428571429 Combine like terms: 7.95394909 + 1.428571429 = 9.382520519 t = 9.382520519 Simplifying t = 9.382520519Subproblem 2
t + -1.428571429 = -7.95394909 Simplifying t + -1.428571429 = -7.95394909 Reorder the terms: -1.428571429 + t = -7.95394909 Solving -1.428571429 + t = -7.95394909 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.428571429' to each side of the equation. -1.428571429 + 1.428571429 + t = -7.95394909 + 1.428571429 Combine like terms: -1.428571429 + 1.428571429 = 0.000000000 0.000000000 + t = -7.95394909 + 1.428571429 t = -7.95394909 + 1.428571429 Combine like terms: -7.95394909 + 1.428571429 = -6.525377661 t = -6.525377661 Simplifying t = -6.525377661Solution
The solution to the problem is based on the solutions from the subproblems. t = {9.382520519, -6.525377661}
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