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Simplifying 4.9t2 + 9t + -22 = 0 Reorder the terms: -22 + 9t + 4.9t2 = 0 Solving -22 + 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'. -4.489795918 + 1.836734694t + t2 = 0 Move the constant term to the right: Add '4.489795918' to each side of the equation. -4.489795918 + 1.836734694t + 4.489795918 + t2 = 0 + 4.489795918 Reorder the terms: -4.489795918 + 4.489795918 + 1.836734694t + t2 = 0 + 4.489795918 Combine like terms: -4.489795918 + 4.489795918 = 0.000000000 0.000000000 + 1.836734694t + t2 = 0 + 4.489795918 1.836734694t + t2 = 0 + 4.489795918 Combine like terms: 0 + 4.489795918 = 4.489795918 1.836734694t + t2 = 4.489795918 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 = 4.489795918 + 0.8433985840 Reorder the terms: 0.8433985840 + 1.836734694t + t2 = 4.489795918 + 0.8433985840 Combine like terms: 4.489795918 + 0.8433985840 = 5.333194502 0.8433985840 + 1.836734694t + t2 = 5.333194502 Factor a perfect square on the left side: (t + 0.918367347)(t + 0.918367347) = 5.333194502 Calculate the square root of the right side: 2.309371019 Break this problem into two subproblems by setting (t + 0.918367347) equal to 2.309371019 and -2.309371019.Subproblem 1
t + 0.918367347 = 2.309371019 Simplifying t + 0.918367347 = 2.309371019 Reorder the terms: 0.918367347 + t = 2.309371019 Solving 0.918367347 + t = 2.309371019 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 = 2.309371019 + -0.918367347 Combine like terms: 0.918367347 + -0.918367347 = 0.000000000 0.000000000 + t = 2.309371019 + -0.918367347 t = 2.309371019 + -0.918367347 Combine like terms: 2.309371019 + -0.918367347 = 1.391003672 t = 1.391003672 Simplifying t = 1.391003672Subproblem 2
t + 0.918367347 = -2.309371019 Simplifying t + 0.918367347 = -2.309371019 Reorder the terms: 0.918367347 + t = -2.309371019 Solving 0.918367347 + t = -2.309371019 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 = -2.309371019 + -0.918367347 Combine like terms: 0.918367347 + -0.918367347 = 0.000000000 0.000000000 + t = -2.309371019 + -0.918367347 t = -2.309371019 + -0.918367347 Combine like terms: -2.309371019 + -0.918367347 = -3.227738366 t = -3.227738366 Simplifying t = -3.227738366Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.391003672, -3.227738366}
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