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Simplifying (2x * 2x) + 4x + -9 = 0 Reorder the terms for easier multiplication: (2 * 2x * x) + 4x + -9 = 0 Multiply 2 * 2 (4x * x) + 4x + -9 = 0 Multiply x * x (4x2) + 4x + -9 = 0 Reorder the terms: -9 + 4x + (4x2) = 0 Solving -9 + 4x + (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'. -2.25 + x + x2 = 0 Move the constant term to the right: Add '2.25' to each side of the equation. -2.25 + x + 2.25 + x2 = 0 + 2.25 Reorder the terms: -2.25 + 2.25 + x + x2 = 0 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + x + x2 = 0 + 2.25 x + x2 = 0 + 2.25 Combine like terms: 0 + 2.25 = 2.25 x + x2 = 2.25 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. + 0.25 + x2 = 2.25 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + x2 = 2.25 + 0.25 Combine like terms: 2.25 + 0.25 = 2.5 1.25 + x2 = 2.5 Factor a perfect square on the left side: ((x) + 0.5)((x) + 0.5) = 2.5 Calculate the square root of the right side: 1.58113883 Break this problem into two subproblems by setting ((x) + 0.5) equal to 1.58113883 and -1.58113883.Subproblem 1
(x) + 0.5 = 1.58113883 Simplifying (x) + 0.5 = 1.58113883 x + 0.5 = 1.58113883 Reorder the terms: 0.5 + x = 1.58113883 Solving 0.5 + x = 1.58113883 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 1.58113883 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 1.58113883 + -0.5 x = 1.58113883 + -0.5 Combine like terms: 1.58113883 + -0.5 = 1.08113883 x = 1.08113883 Simplifying x = 1.08113883Subproblem 2
(x) + 0.5 = -1.58113883 Simplifying (x) + 0.5 = -1.58113883 x + 0.5 = -1.58113883 Reorder the terms: 0.5 + x = -1.58113883 Solving 0.5 + x = -1.58113883 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -1.58113883 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -1.58113883 + -0.5 x = -1.58113883 + -0.5 Combine like terms: -1.58113883 + -0.5 = -2.08113883 x = -2.08113883 Simplifying x = -2.08113883Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.08113883, -2.08113883}
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