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Simplifying 23x2 + 30x + 8 = 0 Reorder the terms: 8 + 30x + 23x2 = 0 Solving 8 + 30x + 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 + 1.304347826x + x2 = 0 Move the constant term to the right: Add '-0.347826087' to each side of the equation. 0.347826087 + 1.304347826x + -0.347826087 + x2 = 0 + -0.347826087 Reorder the terms: 0.347826087 + -0.347826087 + 1.304347826x + x2 = 0 + -0.347826087 Combine like terms: 0.347826087 + -0.347826087 = 0.000000000 0.000000000 + 1.304347826x + x2 = 0 + -0.347826087 1.304347826x + x2 = 0 + -0.347826087 Combine like terms: 0 + -0.347826087 = -0.347826087 1.304347826x + x2 = -0.347826087 The x term is 1.304347826x. Take half its coefficient (0.652173913). Square it (0.4253308128) and add it to both sides. Add '0.4253308128' to each side of the equation. 1.304347826x + 0.4253308128 + x2 = -0.347826087 + 0.4253308128 Reorder the terms: 0.4253308128 + 1.304347826x + x2 = -0.347826087 + 0.4253308128 Combine like terms: -0.347826087 + 0.4253308128 = 0.0775047258 0.4253308128 + 1.304347826x + x2 = 0.0775047258 Factor a perfect square on the left side: (x + 0.652173913)(x + 0.652173913) = 0.0775047258 Calculate the square root of the right side: 0.278396706 Break this problem into two subproblems by setting (x + 0.652173913) equal to 0.278396706 and -0.278396706.Subproblem 1
x + 0.652173913 = 0.278396706 Simplifying x + 0.652173913 = 0.278396706 Reorder the terms: 0.652173913 + x = 0.278396706 Solving 0.652173913 + x = 0.278396706 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.652173913' to each side of the equation. 0.652173913 + -0.652173913 + x = 0.278396706 + -0.652173913 Combine like terms: 0.652173913 + -0.652173913 = 0.000000000 0.000000000 + x = 0.278396706 + -0.652173913 x = 0.278396706 + -0.652173913 Combine like terms: 0.278396706 + -0.652173913 = -0.373777207 x = -0.373777207 Simplifying x = -0.373777207Subproblem 2
x + 0.652173913 = -0.278396706 Simplifying x + 0.652173913 = -0.278396706 Reorder the terms: 0.652173913 + x = -0.278396706 Solving 0.652173913 + x = -0.278396706 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.652173913' to each side of the equation. 0.652173913 + -0.652173913 + x = -0.278396706 + -0.652173913 Combine like terms: 0.652173913 + -0.652173913 = 0.000000000 0.000000000 + x = -0.278396706 + -0.652173913 x = -0.278396706 + -0.652173913 Combine like terms: -0.278396706 + -0.652173913 = -0.930570619 x = -0.930570619 Simplifying x = -0.930570619Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.373777207, -0.930570619}
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