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Simplifying -4.9t2 + 24t + 10 = 0 Reorder the terms: 10 + 24t + -4.9t2 = 0 Solving 10 + 24t + -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'. -2.040816327 + -4.897959184t + t2 = 0 Move the constant term to the right: Add '2.040816327' to each side of the equation. -2.040816327 + -4.897959184t + 2.040816327 + t2 = 0 + 2.040816327 Reorder the terms: -2.040816327 + 2.040816327 + -4.897959184t + t2 = 0 + 2.040816327 Combine like terms: -2.040816327 + 2.040816327 = 0.000000000 0.000000000 + -4.897959184t + t2 = 0 + 2.040816327 -4.897959184t + t2 = 0 + 2.040816327 Combine like terms: 0 + 2.040816327 = 2.040816327 -4.897959184t + t2 = 2.040816327 The t term is -4.897959184t. Take half its coefficient (-2.448979592). Square it (5.997501042) and add it to both sides. Add '5.997501042' to each side of the equation. -4.897959184t + 5.997501042 + t2 = 2.040816327 + 5.997501042 Reorder the terms: 5.997501042 + -4.897959184t + t2 = 2.040816327 + 5.997501042 Combine like terms: 2.040816327 + 5.997501042 = 8.038317369 5.997501042 + -4.897959184t + t2 = 8.038317369 Factor a perfect square on the left side: (t + -2.448979592)(t + -2.448979592) = 8.038317369 Calculate the square root of the right side: 2.835192651 Break this problem into two subproblems by setting (t + -2.448979592) equal to 2.835192651 and -2.835192651.Subproblem 1
t + -2.448979592 = 2.835192651 Simplifying t + -2.448979592 = 2.835192651 Reorder the terms: -2.448979592 + t = 2.835192651 Solving -2.448979592 + t = 2.835192651 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.448979592' to each side of the equation. -2.448979592 + 2.448979592 + t = 2.835192651 + 2.448979592 Combine like terms: -2.448979592 + 2.448979592 = 0.000000000 0.000000000 + t = 2.835192651 + 2.448979592 t = 2.835192651 + 2.448979592 Combine like terms: 2.835192651 + 2.448979592 = 5.284172243 t = 5.284172243 Simplifying t = 5.284172243Subproblem 2
t + -2.448979592 = -2.835192651 Simplifying t + -2.448979592 = -2.835192651 Reorder the terms: -2.448979592 + t = -2.835192651 Solving -2.448979592 + t = -2.835192651 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.448979592' to each side of the equation. -2.448979592 + 2.448979592 + t = -2.835192651 + 2.448979592 Combine like terms: -2.448979592 + 2.448979592 = 0.000000000 0.000000000 + t = -2.835192651 + 2.448979592 t = -2.835192651 + 2.448979592 Combine like terms: -2.835192651 + 2.448979592 = -0.386213059 t = -0.386213059 Simplifying t = -0.386213059Solution
The solution to the problem is based on the solutions from the subproblems. t = {5.284172243, -0.386213059}
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