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Simplifying 4.9t2 + -15t + -12 = 0 Reorder the terms: -12 + -15t + 4.9t2 = 0 Solving -12 + -15t + 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'. -2.448979592 + -3.06122449t + t2 = 0 Move the constant term to the right: Add '2.448979592' to each side of the equation. -2.448979592 + -3.06122449t + 2.448979592 + t2 = 0 + 2.448979592 Reorder the terms: -2.448979592 + 2.448979592 + -3.06122449t + t2 = 0 + 2.448979592 Combine like terms: -2.448979592 + 2.448979592 = 0.000000000 0.000000000 + -3.06122449t + t2 = 0 + 2.448979592 -3.06122449t + t2 = 0 + 2.448979592 Combine like terms: 0 + 2.448979592 = 2.448979592 -3.06122449t + t2 = 2.448979592 The t term is -3.06122449t. Take half its coefficient (-1.530612245). Square it (2.342773845) and add it to both sides. Add '2.342773845' to each side of the equation. -3.06122449t + 2.342773845 + t2 = 2.448979592 + 2.342773845 Reorder the terms: 2.342773845 + -3.06122449t + t2 = 2.448979592 + 2.342773845 Combine like terms: 2.448979592 + 2.342773845 = 4.791753437 2.342773845 + -3.06122449t + t2 = 4.791753437 Factor a perfect square on the left side: (t + -1.530612245)(t + -1.530612245) = 4.791753437 Calculate the square root of the right side: 2.189007409 Break this problem into two subproblems by setting (t + -1.530612245) equal to 2.189007409 and -2.189007409.Subproblem 1
t + -1.530612245 = 2.189007409 Simplifying t + -1.530612245 = 2.189007409 Reorder the terms: -1.530612245 + t = 2.189007409 Solving -1.530612245 + t = 2.189007409 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.530612245' to each side of the equation. -1.530612245 + 1.530612245 + t = 2.189007409 + 1.530612245 Combine like terms: -1.530612245 + 1.530612245 = 0.000000000 0.000000000 + t = 2.189007409 + 1.530612245 t = 2.189007409 + 1.530612245 Combine like terms: 2.189007409 + 1.530612245 = 3.719619654 t = 3.719619654 Simplifying t = 3.719619654Subproblem 2
t + -1.530612245 = -2.189007409 Simplifying t + -1.530612245 = -2.189007409 Reorder the terms: -1.530612245 + t = -2.189007409 Solving -1.530612245 + t = -2.189007409 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.530612245' to each side of the equation. -1.530612245 + 1.530612245 + t = -2.189007409 + 1.530612245 Combine like terms: -1.530612245 + 1.530612245 = 0.000000000 0.000000000 + t = -2.189007409 + 1.530612245 t = -2.189007409 + 1.530612245 Combine like terms: -2.189007409 + 1.530612245 = -0.658395164 t = -0.658395164 Simplifying t = -0.658395164Solution
The solution to the problem is based on the solutions from the subproblems. t = {3.719619654, -0.658395164}
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