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Simplifying 0.22 = (x + -112250 + -70200) * x Reorder the terms: 0.22 = (-112250 + -70200 + x) * x Combine like terms: -112250 + -70200 = -182450 0.22 = (-182450 + x) * x Reorder the terms for easier multiplication: 0.22 = x(-182450 + x) 0.22 = (-182450 * x + x * x) 0.22 = (-182450x + x2) Solving 0.22 = -182450x + x2 Solving for variable 'x'. Reorder the terms: 0.22 + 182450x + -1x2 = -182450x + 182450x + x2 + -1x2 Combine like terms: -182450x + 182450x = 0 0.22 + 182450x + -1x2 = 0 + x2 + -1x2 0.22 + 182450x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 0.22 + 182450x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -0.22 + -182450x + x2 = 0 Move the constant term to the right: Add '0.22' to each side of the equation. -0.22 + -182450x + 0.22 + x2 = 0 + 0.22 Reorder the terms: -0.22 + 0.22 + -182450x + x2 = 0 + 0.22 Combine like terms: -0.22 + 0.22 = 0.00 0.00 + -182450x + x2 = 0 + 0.22 -182450x + x2 = 0 + 0.22 Combine like terms: 0 + 0.22 = 0.22 -182450x + x2 = 0.22 The x term is -182450x. Take half its coefficient (-91225). Square it (8322000625) and add it to both sides. Add '8322000625' to each side of the equation. -182450x + 8322000625 + x2 = 0.22 + 8322000625 Reorder the terms: 8322000625 + -182450x + x2 = 0.22 + 8322000625 Combine like terms: 0.22 + 8322000625 = 8322000625.22 8322000625 + -182450x + x2 = 8322000625.22 Factor a perfect square on the left side: (x + -91225)(x + -91225) = 8322000625.22 Calculate the square root of the right side: 91225.000001206 Break this problem into two subproblems by setting (x + -91225) equal to 91225.000001206 and -91225.000001206.Subproblem 1
x + -91225 = 91225.000001206 Simplifying x + -91225 = 91225.000001206 Reorder the terms: -91225 + x = 91225.000001206 Solving -91225 + x = 91225.000001206 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '91225' to each side of the equation. -91225 + 91225 + x = 91225.000001206 + 91225 Combine like terms: -91225 + 91225 = 0 0 + x = 91225.000001206 + 91225 x = 91225.000001206 + 91225 Combine like terms: 91225.000001206 + 91225 = 182450.000001206 x = 182450.000001206 Simplifying x = 182450.000001206Subproblem 2
x + -91225 = -91225.000001206 Simplifying x + -91225 = -91225.000001206 Reorder the terms: -91225 + x = -91225.000001206 Solving -91225 + x = -91225.000001206 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '91225' to each side of the equation. -91225 + 91225 + x = -91225.000001206 + 91225 Combine like terms: -91225 + 91225 = 0 0 + x = -91225.000001206 + 91225 x = -91225.000001206 + 91225 Combine like terms: -91225.000001206 + 91225 = -0.000001206 x = -0.000001206 Simplifying x = -0.000001206Solution
The solution to the problem is based on the solutions from the subproblems. x = {182450.000001206, -0.000001206}
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