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Simplifying -4.9t2 + 34t + 0.91 = 0 Reorder the terms: 0.91 + 34t + -4.9t2 = 0 Solving 0.91 + 34t + -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'. -0.1857142857 + -6.93877551t + t2 = 0 Move the constant term to the right: Add '0.1857142857' to each side of the equation. -0.1857142857 + -6.93877551t + 0.1857142857 + t2 = 0 + 0.1857142857 Reorder the terms: -0.1857142857 + 0.1857142857 + -6.93877551t + t2 = 0 + 0.1857142857 Combine like terms: -0.1857142857 + 0.1857142857 = 0.0000000000 0.0000000000 + -6.93877551t + t2 = 0 + 0.1857142857 -6.93877551t + t2 = 0 + 0.1857142857 Combine like terms: 0 + 0.1857142857 = 0.1857142857 -6.93877551t + t2 = 0.1857142857 The t term is -6.93877551t. Take half its coefficient (-3.469387755). Square it (12.03665139) and add it to both sides. Add '12.03665139' to each side of the equation. -6.93877551t + 12.03665139 + t2 = 0.1857142857 + 12.03665139 Reorder the terms: 12.03665139 + -6.93877551t + t2 = 0.1857142857 + 12.03665139 Combine like terms: 0.1857142857 + 12.03665139 = 12.2223656757 12.03665139 + -6.93877551t + t2 = 12.2223656757 Factor a perfect square on the left side: (t + -3.469387755)(t + -3.469387755) = 12.2223656757 Calculate the square root of the right side: 3.49605001 Break this problem into two subproblems by setting (t + -3.469387755) equal to 3.49605001 and -3.49605001.Subproblem 1
t + -3.469387755 = 3.49605001 Simplifying t + -3.469387755 = 3.49605001 Reorder the terms: -3.469387755 + t = 3.49605001 Solving -3.469387755 + t = 3.49605001 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3.469387755' to each side of the equation. -3.469387755 + 3.469387755 + t = 3.49605001 + 3.469387755 Combine like terms: -3.469387755 + 3.469387755 = 0.000000000 0.000000000 + t = 3.49605001 + 3.469387755 t = 3.49605001 + 3.469387755 Combine like terms: 3.49605001 + 3.469387755 = 6.965437765 t = 6.965437765 Simplifying t = 6.965437765Subproblem 2
t + -3.469387755 = -3.49605001 Simplifying t + -3.469387755 = -3.49605001 Reorder the terms: -3.469387755 + t = -3.49605001 Solving -3.469387755 + t = -3.49605001 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3.469387755' to each side of the equation. -3.469387755 + 3.469387755 + t = -3.49605001 + 3.469387755 Combine like terms: -3.469387755 + 3.469387755 = 0.000000000 0.000000000 + t = -3.49605001 + 3.469387755 t = -3.49605001 + 3.469387755 Combine like terms: -3.49605001 + 3.469387755 = -0.026662255 t = -0.026662255 Simplifying t = -0.026662255Solution
The solution to the problem is based on the solutions from the subproblems. t = {6.965437765, -0.026662255}
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