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Simplifying 23x + -6 = 4x2 Reorder the terms: -6 + 23x = 4x2 Solving -6 + 23x = 4x2 Solving for variable 'x'. Combine like terms: 4x2 + -4x2 = 0 -6 + 23x + -4x2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. 1.5 + -5.75x + x2 = 0 Move the constant term to the right: Add '-1.5' to each side of the equation. 1.5 + -5.75x + -1.5 + x2 = 0 + -1.5 Reorder the terms: 1.5 + -1.5 + -5.75x + x2 = 0 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + -5.75x + x2 = 0 + -1.5 -5.75x + x2 = 0 + -1.5 Combine like terms: 0 + -1.5 = -1.5 -5.75x + x2 = -1.5 The x term is -5.75x. Take half its coefficient (-2.875). Square it (8.265625) and add it to both sides. Add '8.265625' to each side of the equation. -5.75x + 8.265625 + x2 = -1.5 + 8.265625 Reorder the terms: 8.265625 + -5.75x + x2 = -1.5 + 8.265625 Combine like terms: -1.5 + 8.265625 = 6.765625 8.265625 + -5.75x + x2 = 6.765625 Factor a perfect square on the left side: (x + -2.875)(x + -2.875) = 6.765625 Calculate the square root of the right side: 2.601081506 Break this problem into two subproblems by setting (x + -2.875) equal to 2.601081506 and -2.601081506.Subproblem 1
x + -2.875 = 2.601081506 Simplifying x + -2.875 = 2.601081506 Reorder the terms: -2.875 + x = 2.601081506 Solving -2.875 + x = 2.601081506 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.875' to each side of the equation. -2.875 + 2.875 + x = 2.601081506 + 2.875 Combine like terms: -2.875 + 2.875 = 0.000 0.000 + x = 2.601081506 + 2.875 x = 2.601081506 + 2.875 Combine like terms: 2.601081506 + 2.875 = 5.476081506 x = 5.476081506 Simplifying x = 5.476081506Subproblem 2
x + -2.875 = -2.601081506 Simplifying x + -2.875 = -2.601081506 Reorder the terms: -2.875 + x = -2.601081506 Solving -2.875 + x = -2.601081506 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.875' to each side of the equation. -2.875 + 2.875 + x = -2.601081506 + 2.875 Combine like terms: -2.875 + 2.875 = 0.000 0.000 + x = -2.601081506 + 2.875 x = -2.601081506 + 2.875 Combine like terms: -2.601081506 + 2.875 = 0.273918494 x = 0.273918494 Simplifying x = 0.273918494Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.476081506, 0.273918494}
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