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Simplifying 33x2 + -32x + -585 = 0 Reorder the terms: -585 + -32x + 33x2 = 0 Solving -585 + -32x + 33x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 33 the coefficient of the squared term: Divide each side by '33'. -17.72727273 + -0.9696969697x + x2 = 0 Move the constant term to the right: Add '17.72727273' to each side of the equation. -17.72727273 + -0.9696969697x + 17.72727273 + x2 = 0 + 17.72727273 Reorder the terms: -17.72727273 + 17.72727273 + -0.9696969697x + x2 = 0 + 17.72727273 Combine like terms: -17.72727273 + 17.72727273 = 0.00000000 0.00000000 + -0.9696969697x + x2 = 0 + 17.72727273 -0.9696969697x + x2 = 0 + 17.72727273 Combine like terms: 0 + 17.72727273 = 17.72727273 -0.9696969697x + x2 = 17.72727273 The x term is -0.9696969697x. Take half its coefficient (-0.4848484849). Square it (0.2350780533) and add it to both sides. Add '0.2350780533' to each side of the equation. -0.9696969697x + 0.2350780533 + x2 = 17.72727273 + 0.2350780533 Reorder the terms: 0.2350780533 + -0.9696969697x + x2 = 17.72727273 + 0.2350780533 Combine like terms: 17.72727273 + 0.2350780533 = 17.9623507833 0.2350780533 + -0.9696969697x + x2 = 17.9623507833 Factor a perfect square on the left side: (x + -0.4848484849)(x + -0.4848484849) = 17.9623507833 Calculate the square root of the right side: 4.238201362 Break this problem into two subproblems by setting (x + -0.4848484849) equal to 4.238201362 and -4.238201362.Subproblem 1
x + -0.4848484849 = 4.238201362 Simplifying x + -0.4848484849 = 4.238201362 Reorder the terms: -0.4848484849 + x = 4.238201362 Solving -0.4848484849 + x = 4.238201362 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4848484849' to each side of the equation. -0.4848484849 + 0.4848484849 + x = 4.238201362 + 0.4848484849 Combine like terms: -0.4848484849 + 0.4848484849 = 0.0000000000 0.0000000000 + x = 4.238201362 + 0.4848484849 x = 4.238201362 + 0.4848484849 Combine like terms: 4.238201362 + 0.4848484849 = 4.7230498469 x = 4.7230498469 Simplifying x = 4.7230498469Subproblem 2
x + -0.4848484849 = -4.238201362 Simplifying x + -0.4848484849 = -4.238201362 Reorder the terms: -0.4848484849 + x = -4.238201362 Solving -0.4848484849 + x = -4.238201362 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4848484849' to each side of the equation. -0.4848484849 + 0.4848484849 + x = -4.238201362 + 0.4848484849 Combine like terms: -0.4848484849 + 0.4848484849 = 0.0000000000 0.0000000000 + x = -4.238201362 + 0.4848484849 x = -4.238201362 + 0.4848484849 Combine like terms: -4.238201362 + 0.4848484849 = -3.7533528771 x = -3.7533528771 Simplifying x = -3.7533528771Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.7230498469, -3.7533528771}
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