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Simplifying 4.9t2 + 9t + -950 = 0 Reorder the terms: -950 + 9t + 4.9t2 = 0 Solving -950 + 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'. -193.877551 + 1.836734694t + t2 = 0 Move the constant term to the right: Add '193.877551' to each side of the equation. -193.877551 + 1.836734694t + 193.877551 + t2 = 0 + 193.877551 Reorder the terms: -193.877551 + 193.877551 + 1.836734694t + t2 = 0 + 193.877551 Combine like terms: -193.877551 + 193.877551 = 0.000000 0.000000 + 1.836734694t + t2 = 0 + 193.877551 1.836734694t + t2 = 0 + 193.877551 Combine like terms: 0 + 193.877551 = 193.877551 1.836734694t + t2 = 193.877551 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 = 193.877551 + 0.8433985840 Reorder the terms: 0.8433985840 + 1.836734694t + t2 = 193.877551 + 0.8433985840 Combine like terms: 193.877551 + 0.8433985840 = 194.720949584 0.8433985840 + 1.836734694t + t2 = 194.720949584 Factor a perfect square on the left side: (t + 0.918367347)(t + 0.918367347) = 194.720949584 Calculate the square root of the right side: 13.954244859 Break this problem into two subproblems by setting (t + 0.918367347) equal to 13.954244859 and -13.954244859.Subproblem 1
t + 0.918367347 = 13.954244859 Simplifying t + 0.918367347 = 13.954244859 Reorder the terms: 0.918367347 + t = 13.954244859 Solving 0.918367347 + t = 13.954244859 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 = 13.954244859 + -0.918367347 Combine like terms: 0.918367347 + -0.918367347 = 0.000000000 0.000000000 + t = 13.954244859 + -0.918367347 t = 13.954244859 + -0.918367347 Combine like terms: 13.954244859 + -0.918367347 = 13.035877512 t = 13.035877512 Simplifying t = 13.035877512Subproblem 2
t + 0.918367347 = -13.954244859 Simplifying t + 0.918367347 = -13.954244859 Reorder the terms: 0.918367347 + t = -13.954244859 Solving 0.918367347 + t = -13.954244859 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 = -13.954244859 + -0.918367347 Combine like terms: 0.918367347 + -0.918367347 = 0.000000000 0.000000000 + t = -13.954244859 + -0.918367347 t = -13.954244859 + -0.918367347 Combine like terms: -13.954244859 + -0.918367347 = -14.872612206 t = -14.872612206 Simplifying t = -14.872612206Solution
The solution to the problem is based on the solutions from the subproblems. t = {13.035877512, -14.872612206}
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