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Simplifying -4.9t2 + 9t + 500 = 0 Reorder the terms: 500 + 9t + -4.9t2 = 0 Solving 500 + 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'. -102.0408163 + -1.836734694t + t2 = 0 Move the constant term to the right: Add '102.0408163' to each side of the equation. -102.0408163 + -1.836734694t + 102.0408163 + t2 = 0 + 102.0408163 Reorder the terms: -102.0408163 + 102.0408163 + -1.836734694t + t2 = 0 + 102.0408163 Combine like terms: -102.0408163 + 102.0408163 = 0.0000000 0.0000000 + -1.836734694t + t2 = 0 + 102.0408163 -1.836734694t + t2 = 0 + 102.0408163 Combine like terms: 0 + 102.0408163 = 102.0408163 -1.836734694t + t2 = 102.0408163 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 = 102.0408163 + 0.8433985840 Reorder the terms: 0.8433985840 + -1.836734694t + t2 = 102.0408163 + 0.8433985840 Combine like terms: 102.0408163 + 0.8433985840 = 102.884214884 0.8433985840 + -1.836734694t + t2 = 102.884214884 Factor a perfect square on the left side: (t + -0.918367347)(t + -0.918367347) = 102.884214884 Calculate the square root of the right side: 10.143185638 Break this problem into two subproblems by setting (t + -0.918367347) equal to 10.143185638 and -10.143185638.Subproblem 1
t + -0.918367347 = 10.143185638 Simplifying t + -0.918367347 = 10.143185638 Reorder the terms: -0.918367347 + t = 10.143185638 Solving -0.918367347 + t = 10.143185638 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 = 10.143185638 + 0.918367347 Combine like terms: -0.918367347 + 0.918367347 = 0.000000000 0.000000000 + t = 10.143185638 + 0.918367347 t = 10.143185638 + 0.918367347 Combine like terms: 10.143185638 + 0.918367347 = 11.061552985 t = 11.061552985 Simplifying t = 11.061552985Subproblem 2
t + -0.918367347 = -10.143185638 Simplifying t + -0.918367347 = -10.143185638 Reorder the terms: -0.918367347 + t = -10.143185638 Solving -0.918367347 + t = -10.143185638 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 = -10.143185638 + 0.918367347 Combine like terms: -0.918367347 + 0.918367347 = 0.000000000 0.000000000 + t = -10.143185638 + 0.918367347 t = -10.143185638 + 0.918367347 Combine like terms: -10.143185638 + 0.918367347 = -9.224818291 t = -9.224818291 Simplifying t = -9.224818291Solution
The solution to the problem is based on the solutions from the subproblems. t = {11.061552985, -9.224818291}
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