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Simplifying 200x2 + -12x + -18.4 = 0 Reorder the terms: -18.4 + -12x + 200x2 = 0 Solving -18.4 + -12x + 200x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 200 the coefficient of the squared term: Divide each side by '200'. -0.092 + -0.06x + x2 = 0 Move the constant term to the right: Add '0.092' to each side of the equation. -0.092 + -0.06x + 0.092 + x2 = 0 + 0.092 Reorder the terms: -0.092 + 0.092 + -0.06x + x2 = 0 + 0.092 Combine like terms: -0.092 + 0.092 = 0.000 0.000 + -0.06x + x2 = 0 + 0.092 -0.06x + x2 = 0 + 0.092 Combine like terms: 0 + 0.092 = 0.092 -0.06x + x2 = 0.092 The x term is -0.06x. Take half its coefficient (-0.03). Square it (0.0009) and add it to both sides. Add '0.0009' to each side of the equation. -0.06x + 0.0009 + x2 = 0.092 + 0.0009 Reorder the terms: 0.0009 + -0.06x + x2 = 0.092 + 0.0009 Combine like terms: 0.092 + 0.0009 = 0.0929 0.0009 + -0.06x + x2 = 0.0929 Factor a perfect square on the left side: (x + -0.03)(x + -0.03) = 0.0929 Calculate the square root of the right side: 0.304795013 Break this problem into two subproblems by setting (x + -0.03) equal to 0.304795013 and -0.304795013.Subproblem 1
x + -0.03 = 0.304795013 Simplifying x + -0.03 = 0.304795013 Reorder the terms: -0.03 + x = 0.304795013 Solving -0.03 + x = 0.304795013 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.03' to each side of the equation. -0.03 + 0.03 + x = 0.304795013 + 0.03 Combine like terms: -0.03 + 0.03 = 0.00 0.00 + x = 0.304795013 + 0.03 x = 0.304795013 + 0.03 Combine like terms: 0.304795013 + 0.03 = 0.334795013 x = 0.334795013 Simplifying x = 0.334795013Subproblem 2
x + -0.03 = -0.304795013 Simplifying x + -0.03 = -0.304795013 Reorder the terms: -0.03 + x = -0.304795013 Solving -0.03 + x = -0.304795013 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.03' to each side of the equation. -0.03 + 0.03 + x = -0.304795013 + 0.03 Combine like terms: -0.03 + 0.03 = 0.00 0.00 + x = -0.304795013 + 0.03 x = -0.304795013 + 0.03 Combine like terms: -0.304795013 + 0.03 = -0.274795013 x = -0.274795013 Simplifying x = -0.274795013Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.334795013, -0.274795013}
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