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Simplifying 22.143 + -322.3x + 1100x2 = 0 Solving 22.143 + -322.3x + 1100x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 1100 the coefficient of the squared term: Divide each side by '1100'. 0.02013 + -0.293x + x2 = 0 Move the constant term to the right: Add '-0.02013' to each side of the equation. 0.02013 + -0.293x + -0.02013 + x2 = 0 + -0.02013 Reorder the terms: 0.02013 + -0.02013 + -0.293x + x2 = 0 + -0.02013 Combine like terms: 0.02013 + -0.02013 = 0.00000 0.00000 + -0.293x + x2 = 0 + -0.02013 -0.293x + x2 = 0 + -0.02013 Combine like terms: 0 + -0.02013 = -0.02013 -0.293x + x2 = -0.02013 The x term is -0.293x. Take half its coefficient (-0.1465). Square it (0.02146225) and add it to both sides. Add '0.02146225' to each side of the equation. -0.293x + 0.02146225 + x2 = -0.02013 + 0.02146225 Reorder the terms: 0.02146225 + -0.293x + x2 = -0.02013 + 0.02146225 Combine like terms: -0.02013 + 0.02146225 = 0.00133225 0.02146225 + -0.293x + x2 = 0.00133225 Factor a perfect square on the left side: (x + -0.1465)(x + -0.1465) = 0.00133225 Calculate the square root of the right side: 0.0365 Break this problem into two subproblems by setting (x + -0.1465) equal to 0.0365 and -0.0365.Subproblem 1
x + -0.1465 = 0.0365 Simplifying x + -0.1465 = 0.0365 Reorder the terms: -0.1465 + x = 0.0365 Solving -0.1465 + x = 0.0365 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1465' to each side of the equation. -0.1465 + 0.1465 + x = 0.0365 + 0.1465 Combine like terms: -0.1465 + 0.1465 = 0.0000 0.0000 + x = 0.0365 + 0.1465 x = 0.0365 + 0.1465 Combine like terms: 0.0365 + 0.1465 = 0.183 x = 0.183 Simplifying x = 0.183Subproblem 2
x + -0.1465 = -0.0365 Simplifying x + -0.1465 = -0.0365 Reorder the terms: -0.1465 + x = -0.0365 Solving -0.1465 + x = -0.0365 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1465' to each side of the equation. -0.1465 + 0.1465 + x = -0.0365 + 0.1465 Combine like terms: -0.1465 + 0.1465 = 0.0000 0.0000 + x = -0.0365 + 0.1465 x = -0.0365 + 0.1465 Combine like terms: -0.0365 + 0.1465 = 0.11 x = 0.11 Simplifying x = 0.11Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.183, 0.11}
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