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Simplifying -4.9t2 + 12t + 10 = 0 Reorder the terms: 10 + 12t + -4.9t2 = 0 Solving 10 + 12t + -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 + -2.448979592t + t2 = 0 Move the constant term to the right: Add '2.040816327' to each side of the equation. -2.040816327 + -2.448979592t + 2.040816327 + t2 = 0 + 2.040816327 Reorder the terms: -2.040816327 + 2.040816327 + -2.448979592t + t2 = 0 + 2.040816327 Combine like terms: -2.040816327 + 2.040816327 = 0.000000000 0.000000000 + -2.448979592t + t2 = 0 + 2.040816327 -2.448979592t + t2 = 0 + 2.040816327 Combine like terms: 0 + 2.040816327 = 2.040816327 -2.448979592t + t2 = 2.040816327 The t term is -2.448979592t. Take half its coefficient (-1.224489796). Square it (1.499375261) and add it to both sides. Add '1.499375261' to each side of the equation. -2.448979592t + 1.499375261 + t2 = 2.040816327 + 1.499375261 Reorder the terms: 1.499375261 + -2.448979592t + t2 = 2.040816327 + 1.499375261 Combine like terms: 2.040816327 + 1.499375261 = 3.540191588 1.499375261 + -2.448979592t + t2 = 3.540191588 Factor a perfect square on the left side: (t + -1.224489796)(t + -1.224489796) = 3.540191588 Calculate the square root of the right side: 1.881539685 Break this problem into two subproblems by setting (t + -1.224489796) equal to 1.881539685 and -1.881539685.Subproblem 1
t + -1.224489796 = 1.881539685 Simplifying t + -1.224489796 = 1.881539685 Reorder the terms: -1.224489796 + t = 1.881539685 Solving -1.224489796 + t = 1.881539685 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.224489796' to each side of the equation. -1.224489796 + 1.224489796 + t = 1.881539685 + 1.224489796 Combine like terms: -1.224489796 + 1.224489796 = 0.000000000 0.000000000 + t = 1.881539685 + 1.224489796 t = 1.881539685 + 1.224489796 Combine like terms: 1.881539685 + 1.224489796 = 3.106029481 t = 3.106029481 Simplifying t = 3.106029481Subproblem 2
t + -1.224489796 = -1.881539685 Simplifying t + -1.224489796 = -1.881539685 Reorder the terms: -1.224489796 + t = -1.881539685 Solving -1.224489796 + t = -1.881539685 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.224489796' to each side of the equation. -1.224489796 + 1.224489796 + t = -1.881539685 + 1.224489796 Combine like terms: -1.224489796 + 1.224489796 = 0.000000000 0.000000000 + t = -1.881539685 + 1.224489796 t = -1.881539685 + 1.224489796 Combine like terms: -1.881539685 + 1.224489796 = -0.657049889 t = -0.657049889 Simplifying t = -0.657049889Solution
The solution to the problem is based on the solutions from the subproblems. t = {3.106029481, -0.657049889}
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