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Simplifying 0 = 2x2 + -6x + -23 Reorder the terms: 0 = -23 + -6x + 2x2 Solving 0 = -23 + -6x + 2x2 Solving for variable 'x'. Combine like terms: 0 + 23 = 23 23 + 6x + -2x2 = -23 + -6x + 2x2 + 23 + 6x + -2x2 Reorder the terms: 23 + 6x + -2x2 = -23 + 23 + -6x + 6x + 2x2 + -2x2 Combine like terms: -23 + 23 = 0 23 + 6x + -2x2 = 0 + -6x + 6x + 2x2 + -2x2 23 + 6x + -2x2 = -6x + 6x + 2x2 + -2x2 Combine like terms: -6x + 6x = 0 23 + 6x + -2x2 = 0 + 2x2 + -2x2 23 + 6x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 23 + 6x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -11.5 + -3x + x2 = 0 Move the constant term to the right: Add '11.5' to each side of the equation. -11.5 + -3x + 11.5 + x2 = 0 + 11.5 Reorder the terms: -11.5 + 11.5 + -3x + x2 = 0 + 11.5 Combine like terms: -11.5 + 11.5 = 0.0 0.0 + -3x + x2 = 0 + 11.5 -3x + x2 = 0 + 11.5 Combine like terms: 0 + 11.5 = 11.5 -3x + x2 = 11.5 The x term is -3x. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3x + 2.25 + x2 = 11.5 + 2.25 Reorder the terms: 2.25 + -3x + x2 = 11.5 + 2.25 Combine like terms: 11.5 + 2.25 = 13.75 2.25 + -3x + x2 = 13.75 Factor a perfect square on the left side: (x + -1.5)(x + -1.5) = 13.75 Calculate the square root of the right side: 3.708099244 Break this problem into two subproblems by setting (x + -1.5) equal to 3.708099244 and -3.708099244.Subproblem 1
x + -1.5 = 3.708099244 Simplifying x + -1.5 = 3.708099244 Reorder the terms: -1.5 + x = 3.708099244 Solving -1.5 + x = 3.708099244 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = 3.708099244 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 3.708099244 + 1.5 x = 3.708099244 + 1.5 Combine like terms: 3.708099244 + 1.5 = 5.208099244 x = 5.208099244 Simplifying x = 5.208099244Subproblem 2
x + -1.5 = -3.708099244 Simplifying x + -1.5 = -3.708099244 Reorder the terms: -1.5 + x = -3.708099244 Solving -1.5 + x = -3.708099244 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = -3.708099244 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -3.708099244 + 1.5 x = -3.708099244 + 1.5 Combine like terms: -3.708099244 + 1.5 = -2.208099244 x = -2.208099244 Simplifying x = -2.208099244Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.208099244, -2.208099244}
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