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Simplifying 5x2 = 23x + 6 Reorder the terms: 5x2 = 6 + 23x Solving 5x2 = 6 + 23x Solving for variable 'x'. Reorder the terms: -6 + -23x + 5x2 = 6 + 23x + -6 + -23x Reorder the terms: -6 + -23x + 5x2 = 6 + -6 + 23x + -23x Combine like terms: 6 + -6 = 0 -6 + -23x + 5x2 = 0 + 23x + -23x -6 + -23x + 5x2 = 23x + -23x Combine like terms: 23x + -23x = 0 -6 + -23x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -1.2 + -4.6x + x2 = 0 Move the constant term to the right: Add '1.2' to each side of the equation. -1.2 + -4.6x + 1.2 + x2 = 0 + 1.2 Reorder the terms: -1.2 + 1.2 + -4.6x + x2 = 0 + 1.2 Combine like terms: -1.2 + 1.2 = 0.0 0.0 + -4.6x + x2 = 0 + 1.2 -4.6x + x2 = 0 + 1.2 Combine like terms: 0 + 1.2 = 1.2 -4.6x + x2 = 1.2 The x term is -4.6x. Take half its coefficient (-2.3). Square it (5.29) and add it to both sides. Add '5.29' to each side of the equation. -4.6x + 5.29 + x2 = 1.2 + 5.29 Reorder the terms: 5.29 + -4.6x + x2 = 1.2 + 5.29 Combine like terms: 1.2 + 5.29 = 6.49 5.29 + -4.6x + x2 = 6.49 Factor a perfect square on the left side: (x + -2.3)(x + -2.3) = 6.49 Calculate the square root of the right side: 2.547547841 Break this problem into two subproblems by setting (x + -2.3) equal to 2.547547841 and -2.547547841.Subproblem 1
x + -2.3 = 2.547547841 Simplifying x + -2.3 = 2.547547841 Reorder the terms: -2.3 + x = 2.547547841 Solving -2.3 + x = 2.547547841 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.3' to each side of the equation. -2.3 + 2.3 + x = 2.547547841 + 2.3 Combine like terms: -2.3 + 2.3 = 0.0 0.0 + x = 2.547547841 + 2.3 x = 2.547547841 + 2.3 Combine like terms: 2.547547841 + 2.3 = 4.847547841 x = 4.847547841 Simplifying x = 4.847547841Subproblem 2
x + -2.3 = -2.547547841 Simplifying x + -2.3 = -2.547547841 Reorder the terms: -2.3 + x = -2.547547841 Solving -2.3 + x = -2.547547841 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.3' to each side of the equation. -2.3 + 2.3 + x = -2.547547841 + 2.3 Combine like terms: -2.3 + 2.3 = 0.0 0.0 + x = -2.547547841 + 2.3 x = -2.547547841 + 2.3 Combine like terms: -2.547547841 + 2.3 = -0.247547841 x = -0.247547841 Simplifying x = -0.247547841Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.847547841, -0.247547841}
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