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Simplifying 5x2 + -23x + 2 = 0 Reorder the terms: 2 + -23x + 5x2 = 0 Solving 2 + -23x + 5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 0.4 + -4.6x + x2 = 0 Move the constant term to the right: Add '-0.4' to each side of the equation. 0.4 + -4.6x + -0.4 + x2 = 0 + -0.4 Reorder the terms: 0.4 + -0.4 + -4.6x + x2 = 0 + -0.4 Combine like terms: 0.4 + -0.4 = 0.0 0.0 + -4.6x + x2 = 0 + -0.4 -4.6x + x2 = 0 + -0.4 Combine like terms: 0 + -0.4 = -0.4 -4.6x + x2 = -0.4 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 = -0.4 + 5.29 Reorder the terms: 5.29 + -4.6x + x2 = -0.4 + 5.29 Combine like terms: -0.4 + 5.29 = 4.89 5.29 + -4.6x + x2 = 4.89 Factor a perfect square on the left side: (x + -2.3)(x + -2.3) = 4.89 Calculate the square root of the right side: 2.211334439 Break this problem into two subproblems by setting (x + -2.3) equal to 2.211334439 and -2.211334439.Subproblem 1
x + -2.3 = 2.211334439 Simplifying x + -2.3 = 2.211334439 Reorder the terms: -2.3 + x = 2.211334439 Solving -2.3 + x = 2.211334439 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 = 2.211334439 + 2.3 Combine like terms: -2.3 + 2.3 = 0.0 0.0 + x = 2.211334439 + 2.3 x = 2.211334439 + 2.3 Combine like terms: 2.211334439 + 2.3 = 4.511334439 x = 4.511334439 Simplifying x = 4.511334439Subproblem 2
x + -2.3 = -2.211334439 Simplifying x + -2.3 = -2.211334439 Reorder the terms: -2.3 + x = -2.211334439 Solving -2.3 + x = -2.211334439 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 = -2.211334439 + 2.3 Combine like terms: -2.3 + 2.3 = 0.0 0.0 + x = -2.211334439 + 2.3 x = -2.211334439 + 2.3 Combine like terms: -2.211334439 + 2.3 = 0.088665561 x = 0.088665561 Simplifying x = 0.088665561Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.511334439, 0.088665561}
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