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Simplifying 4x2 + -18x + -1 = 0 Reorder the terms: -1 + -18x + 4x2 = 0 Solving -1 + -18x + 4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -0.25 + -4.5x + x2 = 0 Move the constant term to the right: Add '0.25' to each side of the equation. -0.25 + -4.5x + 0.25 + x2 = 0 + 0.25 Reorder the terms: -0.25 + 0.25 + -4.5x + x2 = 0 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + -4.5x + x2 = 0 + 0.25 -4.5x + x2 = 0 + 0.25 Combine like terms: 0 + 0.25 = 0.25 -4.5x + x2 = 0.25 The x term is -4.5x. Take half its coefficient (-2.25). Square it (5.0625) and add it to both sides. Add '5.0625' to each side of the equation. -4.5x + 5.0625 + x2 = 0.25 + 5.0625 Reorder the terms: 5.0625 + -4.5x + x2 = 0.25 + 5.0625 Combine like terms: 0.25 + 5.0625 = 5.3125 5.0625 + -4.5x + x2 = 5.3125 Factor a perfect square on the left side: (x + -2.25)(x + -2.25) = 5.3125 Calculate the square root of the right side: 2.304886114 Break this problem into two subproblems by setting (x + -2.25) equal to 2.304886114 and -2.304886114.Subproblem 1
x + -2.25 = 2.304886114 Simplifying x + -2.25 = 2.304886114 Reorder the terms: -2.25 + x = 2.304886114 Solving -2.25 + x = 2.304886114 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.25' to each side of the equation. -2.25 + 2.25 + x = 2.304886114 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + x = 2.304886114 + 2.25 x = 2.304886114 + 2.25 Combine like terms: 2.304886114 + 2.25 = 4.554886114 x = 4.554886114 Simplifying x = 4.554886114Subproblem 2
x + -2.25 = -2.304886114 Simplifying x + -2.25 = -2.304886114 Reorder the terms: -2.25 + x = -2.304886114 Solving -2.25 + x = -2.304886114 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.25' to each side of the equation. -2.25 + 2.25 + x = -2.304886114 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + x = -2.304886114 + 2.25 x = -2.304886114 + 2.25 Combine like terms: -2.304886114 + 2.25 = -0.054886114 x = -0.054886114 Simplifying x = -0.054886114Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.554886114, -0.054886114}
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