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Simplifying 4.9t2 + -14t + -70 = 0 Reorder the terms: -70 + -14t + 4.9t2 = 0 Solving -70 + -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'. -14.28571429 + -2.857142857t + t2 = 0 Move the constant term to the right: Add '14.28571429' to each side of the equation. -14.28571429 + -2.857142857t + 14.28571429 + t2 = 0 + 14.28571429 Reorder the terms: -14.28571429 + 14.28571429 + -2.857142857t + t2 = 0 + 14.28571429 Combine like terms: -14.28571429 + 14.28571429 = 0.00000000 0.00000000 + -2.857142857t + t2 = 0 + 14.28571429 -2.857142857t + t2 = 0 + 14.28571429 Combine like terms: 0 + 14.28571429 = 14.28571429 -2.857142857t + t2 = 14.28571429 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 = 14.28571429 + 2.040816328 Reorder the terms: 2.040816328 + -2.857142857t + t2 = 14.28571429 + 2.040816328 Combine like terms: 14.28571429 + 2.040816328 = 16.326530618 2.040816328 + -2.857142857t + t2 = 16.326530618 Factor a perfect square on the left side: (t + -1.428571429)(t + -1.428571429) = 16.326530618 Calculate the square root of the right side: 4.040610179 Break this problem into two subproblems by setting (t + -1.428571429) equal to 4.040610179 and -4.040610179.Subproblem 1
t + -1.428571429 = 4.040610179 Simplifying t + -1.428571429 = 4.040610179 Reorder the terms: -1.428571429 + t = 4.040610179 Solving -1.428571429 + t = 4.040610179 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 = 4.040610179 + 1.428571429 Combine like terms: -1.428571429 + 1.428571429 = 0.000000000 0.000000000 + t = 4.040610179 + 1.428571429 t = 4.040610179 + 1.428571429 Combine like terms: 4.040610179 + 1.428571429 = 5.469181608 t = 5.469181608 Simplifying t = 5.469181608Subproblem 2
t + -1.428571429 = -4.040610179 Simplifying t + -1.428571429 = -4.040610179 Reorder the terms: -1.428571429 + t = -4.040610179 Solving -1.428571429 + t = -4.040610179 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 = -4.040610179 + 1.428571429 Combine like terms: -1.428571429 + 1.428571429 = 0.000000000 0.000000000 + t = -4.040610179 + 1.428571429 t = -4.040610179 + 1.428571429 Combine like terms: -4.040610179 + 1.428571429 = -2.61203875 t = -2.61203875 Simplifying t = -2.61203875Solution
The solution to the problem is based on the solutions from the subproblems. t = {5.469181608, -2.61203875}
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