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Simplifying 182x + -0.02x2 + 18000 = 0 Reorder the terms: 18000 + 182x + -0.02x2 = 0 Solving 18000 + 182x + -0.02x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -0.02 the coefficient of the squared term: Divide each side by '-0.02'. -900000 + -9100x + x2 = 0 Move the constant term to the right: Add '900000' to each side of the equation. -900000 + -9100x + 900000 + x2 = 0 + 900000 Reorder the terms: -900000 + 900000 + -9100x + x2 = 0 + 900000 Combine like terms: -900000 + 900000 = 0 0 + -9100x + x2 = 0 + 900000 -9100x + x2 = 0 + 900000 Combine like terms: 0 + 900000 = 900000 -9100x + x2 = 900000 The x term is -9100x. Take half its coefficient (-4550). Square it (20702500) and add it to both sides. Add '20702500' to each side of the equation. -9100x + 20702500 + x2 = 900000 + 20702500 Reorder the terms: 20702500 + -9100x + x2 = 900000 + 20702500 Combine like terms: 900000 + 20702500 = 21602500 20702500 + -9100x + x2 = 21602500 Factor a perfect square on the left side: (x + -4550)(x + -4550) = 21602500 Calculate the square root of the right side: 4647.848964844 Break this problem into two subproblems by setting (x + -4550) equal to 4647.848964844 and -4647.848964844.Subproblem 1
x + -4550 = 4647.848964844 Simplifying x + -4550 = 4647.848964844 Reorder the terms: -4550 + x = 4647.848964844 Solving -4550 + x = 4647.848964844 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4550' to each side of the equation. -4550 + 4550 + x = 4647.848964844 + 4550 Combine like terms: -4550 + 4550 = 0 0 + x = 4647.848964844 + 4550 x = 4647.848964844 + 4550 Combine like terms: 4647.848964844 + 4550 = 9197.848964844 x = 9197.848964844 Simplifying x = 9197.848964844Subproblem 2
x + -4550 = -4647.848964844 Simplifying x + -4550 = -4647.848964844 Reorder the terms: -4550 + x = -4647.848964844 Solving -4550 + x = -4647.848964844 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4550' to each side of the equation. -4550 + 4550 + x = -4647.848964844 + 4550 Combine like terms: -4550 + 4550 = 0 0 + x = -4647.848964844 + 4550 x = -4647.848964844 + 4550 Combine like terms: -4647.848964844 + 4550 = -97.848964844 x = -97.848964844 Simplifying x = -97.848964844Solution
The solution to the problem is based on the solutions from the subproblems. x = {9197.848964844, -97.848964844}
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