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Simplifying -4.9t2 + -9t + 600 = 0 Reorder the terms: 600 + -9t + -4.9t2 = 0 Solving 600 + -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'. -122.4489796 + 1.836734694t + t2 = 0 Move the constant term to the right: Add '122.4489796' to each side of the equation. -122.4489796 + 1.836734694t + 122.4489796 + t2 = 0 + 122.4489796 Reorder the terms: -122.4489796 + 122.4489796 + 1.836734694t + t2 = 0 + 122.4489796 Combine like terms: -122.4489796 + 122.4489796 = 0.0000000 0.0000000 + 1.836734694t + t2 = 0 + 122.4489796 1.836734694t + t2 = 0 + 122.4489796 Combine like terms: 0 + 122.4489796 = 122.4489796 1.836734694t + t2 = 122.4489796 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 = 122.4489796 + 0.8433985840 Reorder the terms: 0.8433985840 + 1.836734694t + t2 = 122.4489796 + 0.8433985840 Combine like terms: 122.4489796 + 0.8433985840 = 123.292378184 0.8433985840 + 1.836734694t + t2 = 123.292378184 Factor a perfect square on the left side: (t + 0.918367347)(t + 0.918367347) = 123.292378184 Calculate the square root of the right side: 11.103710109 Break this problem into two subproblems by setting (t + 0.918367347) equal to 11.103710109 and -11.103710109.Subproblem 1
t + 0.918367347 = 11.103710109 Simplifying t + 0.918367347 = 11.103710109 Reorder the terms: 0.918367347 + t = 11.103710109 Solving 0.918367347 + t = 11.103710109 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 = 11.103710109 + -0.918367347 Combine like terms: 0.918367347 + -0.918367347 = 0.000000000 0.000000000 + t = 11.103710109 + -0.918367347 t = 11.103710109 + -0.918367347 Combine like terms: 11.103710109 + -0.918367347 = 10.185342762 t = 10.185342762 Simplifying t = 10.185342762Subproblem 2
t + 0.918367347 = -11.103710109 Simplifying t + 0.918367347 = -11.103710109 Reorder the terms: 0.918367347 + t = -11.103710109 Solving 0.918367347 + t = -11.103710109 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 = -11.103710109 + -0.918367347 Combine like terms: 0.918367347 + -0.918367347 = 0.000000000 0.000000000 + t = -11.103710109 + -0.918367347 t = -11.103710109 + -0.918367347 Combine like terms: -11.103710109 + -0.918367347 = -12.022077456 t = -12.022077456 Simplifying t = -12.022077456Solution
The solution to the problem is based on the solutions from the subproblems. t = {10.185342762, -12.022077456}
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