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Simplifying 23x2 + -22x + -8 = 0 Reorder the terms: -8 + -22x + 23x2 = 0 Solving -8 + -22x + 23x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 23 the coefficient of the squared term: Divide each side by '23'. -0.347826087 + -0.9565217391x + x2 = 0 Move the constant term to the right: Add '0.347826087' to each side of the equation. -0.347826087 + -0.9565217391x + 0.347826087 + x2 = 0 + 0.347826087 Reorder the terms: -0.347826087 + 0.347826087 + -0.9565217391x + x2 = 0 + 0.347826087 Combine like terms: -0.347826087 + 0.347826087 = 0.000000000 0.000000000 + -0.9565217391x + x2 = 0 + 0.347826087 -0.9565217391x + x2 = 0 + 0.347826087 Combine like terms: 0 + 0.347826087 = 0.347826087 -0.9565217391x + x2 = 0.347826087 The x term is -0.9565217391x. Take half its coefficient (-0.4782608696). Square it (0.2287334594) and add it to both sides. Add '0.2287334594' to each side of the equation. -0.9565217391x + 0.2287334594 + x2 = 0.347826087 + 0.2287334594 Reorder the terms: 0.2287334594 + -0.9565217391x + x2 = 0.347826087 + 0.2287334594 Combine like terms: 0.347826087 + 0.2287334594 = 0.5765595464 0.2287334594 + -0.9565217391x + x2 = 0.5765595464 Factor a perfect square on the left side: (x + -0.4782608696)(x + -0.4782608696) = 0.5765595464 Calculate the square root of the right side: 0.759315183 Break this problem into two subproblems by setting (x + -0.4782608696) equal to 0.759315183 and -0.759315183.Subproblem 1
x + -0.4782608696 = 0.759315183 Simplifying x + -0.4782608696 = 0.759315183 Reorder the terms: -0.4782608696 + x = 0.759315183 Solving -0.4782608696 + x = 0.759315183 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4782608696' to each side of the equation. -0.4782608696 + 0.4782608696 + x = 0.759315183 + 0.4782608696 Combine like terms: -0.4782608696 + 0.4782608696 = 0.0000000000 0.0000000000 + x = 0.759315183 + 0.4782608696 x = 0.759315183 + 0.4782608696 Combine like terms: 0.759315183 + 0.4782608696 = 1.2375760526 x = 1.2375760526 Simplifying x = 1.2375760526Subproblem 2
x + -0.4782608696 = -0.759315183 Simplifying x + -0.4782608696 = -0.759315183 Reorder the terms: -0.4782608696 + x = -0.759315183 Solving -0.4782608696 + x = -0.759315183 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4782608696' to each side of the equation. -0.4782608696 + 0.4782608696 + x = -0.759315183 + 0.4782608696 Combine like terms: -0.4782608696 + 0.4782608696 = 0.0000000000 0.0000000000 + x = -0.759315183 + 0.4782608696 x = -0.759315183 + 0.4782608696 Combine like terms: -0.759315183 + 0.4782608696 = -0.2810543134 x = -0.2810543134 Simplifying x = -0.2810543134Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.2375760526, -0.2810543134}
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