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Simplifying -4.9t2 + -9t + 550 = 0 Reorder the terms: 550 + -9t + -4.9t2 = 0 Solving 550 + -9t + -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'. -112.244898 + 1.836734694t + t2 = 0 Move the constant term to the right: Add '112.244898' to each side of the equation. -112.244898 + 1.836734694t + 112.244898 + t2 = 0 + 112.244898 Reorder the terms: -112.244898 + 112.244898 + 1.836734694t + t2 = 0 + 112.244898 Combine like terms: -112.244898 + 112.244898 = 0.000000 0.000000 + 1.836734694t + t2 = 0 + 112.244898 1.836734694t + t2 = 0 + 112.244898 Combine like terms: 0 + 112.244898 = 112.244898 1.836734694t + t2 = 112.244898 The t term is 1.836734694t. Take half its coefficient (0.918367347). Square it (0.8433985840) and add it to both sides. Add '0.8433985840' to each side of the equation. 1.836734694t + 0.8433985840 + t2 = 112.244898 + 0.8433985840 Reorder the terms: 0.8433985840 + 1.836734694t + t2 = 112.244898 + 0.8433985840 Combine like terms: 112.244898 + 0.8433985840 = 113.088296584 0.8433985840 + 1.836734694t + t2 = 113.088296584 Factor a perfect square on the left side: (t + 0.918367347)(t + 0.918367347) = 113.088296584 Calculate the square root of the right side: 10.634298124 Break this problem into two subproblems by setting (t + 0.918367347) equal to 10.634298124 and -10.634298124.Subproblem 1
t + 0.918367347 = 10.634298124 Simplifying t + 0.918367347 = 10.634298124 Reorder the terms: 0.918367347 + t = 10.634298124 Solving 0.918367347 + t = 10.634298124 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.918367347' to each side of the equation. 0.918367347 + -0.918367347 + t = 10.634298124 + -0.918367347 Combine like terms: 0.918367347 + -0.918367347 = 0.000000000 0.000000000 + t = 10.634298124 + -0.918367347 t = 10.634298124 + -0.918367347 Combine like terms: 10.634298124 + -0.918367347 = 9.715930777 t = 9.715930777 Simplifying t = 9.715930777Subproblem 2
t + 0.918367347 = -10.634298124 Simplifying t + 0.918367347 = -10.634298124 Reorder the terms: 0.918367347 + t = -10.634298124 Solving 0.918367347 + t = -10.634298124 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.918367347' to each side of the equation. 0.918367347 + -0.918367347 + t = -10.634298124 + -0.918367347 Combine like terms: 0.918367347 + -0.918367347 = 0.000000000 0.000000000 + t = -10.634298124 + -0.918367347 t = -10.634298124 + -0.918367347 Combine like terms: -10.634298124 + -0.918367347 = -11.552665471 t = -11.552665471 Simplifying t = -11.552665471Solution
The solution to the problem is based on the solutions from the subproblems. t = {9.715930777, -11.552665471}
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