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Simplifying -0.009x2 + 4.05x + 2 = 0 Reorder the terms: 2 + 4.05x + -0.009x2 = 0 Solving 2 + 4.05x + -0.009x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -0.009 the coefficient of the squared term: Divide each side by '-0.009'. -222.2222222 + -450x + x2 = 0 Move the constant term to the right: Add '222.2222222' to each side of the equation. -222.2222222 + -450x + 222.2222222 + x2 = 0 + 222.2222222 Reorder the terms: -222.2222222 + 222.2222222 + -450x + x2 = 0 + 222.2222222 Combine like terms: -222.2222222 + 222.2222222 = 0.0000000 0.0000000 + -450x + x2 = 0 + 222.2222222 -450x + x2 = 0 + 222.2222222 Combine like terms: 0 + 222.2222222 = 222.2222222 -450x + x2 = 222.2222222 The x term is -450x. Take half its coefficient (-225). Square it (50625) and add it to both sides. Add '50625' to each side of the equation. -450x + 50625 + x2 = 222.2222222 + 50625 Reorder the terms: 50625 + -450x + x2 = 222.2222222 + 50625 Combine like terms: 222.2222222 + 50625 = 50847.2222222 50625 + -450x + x2 = 50847.2222222 Factor a perfect square on the left side: (x + -225)(x + -225) = 50847.2222222 Calculate the square root of the right side: 225.493286424 Break this problem into two subproblems by setting (x + -225) equal to 225.493286424 and -225.493286424.Subproblem 1
x + -225 = 225.493286424 Simplifying x + -225 = 225.493286424 Reorder the terms: -225 + x = 225.493286424 Solving -225 + x = 225.493286424 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '225' to each side of the equation. -225 + 225 + x = 225.493286424 + 225 Combine like terms: -225 + 225 = 0 0 + x = 225.493286424 + 225 x = 225.493286424 + 225 Combine like terms: 225.493286424 + 225 = 450.493286424 x = 450.493286424 Simplifying x = 450.493286424Subproblem 2
x + -225 = -225.493286424 Simplifying x + -225 = -225.493286424 Reorder the terms: -225 + x = -225.493286424 Solving -225 + x = -225.493286424 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '225' to each side of the equation. -225 + 225 + x = -225.493286424 + 225 Combine like terms: -225 + 225 = 0 0 + x = -225.493286424 + 225 x = -225.493286424 + 225 Combine like terms: -225.493286424 + 225 = -0.493286424 x = -0.493286424 Simplifying x = -0.493286424Solution
The solution to the problem is based on the solutions from the subproblems. x = {450.493286424, -0.493286424}
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