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Simplifying 5x2 + -38x + 23 = 0 Reorder the terms: 23 + -38x + 5x2 = 0 Solving 23 + -38x + 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'. 4.6 + -7.6x + x2 = 0 Move the constant term to the right: Add '-4.6' to each side of the equation. 4.6 + -7.6x + -4.6 + x2 = 0 + -4.6 Reorder the terms: 4.6 + -4.6 + -7.6x + x2 = 0 + -4.6 Combine like terms: 4.6 + -4.6 = 0.0 0.0 + -7.6x + x2 = 0 + -4.6 -7.6x + x2 = 0 + -4.6 Combine like terms: 0 + -4.6 = -4.6 -7.6x + x2 = -4.6 The x term is -7.6x. Take half its coefficient (-3.8). Square it (14.44) and add it to both sides. Add '14.44' to each side of the equation. -7.6x + 14.44 + x2 = -4.6 + 14.44 Reorder the terms: 14.44 + -7.6x + x2 = -4.6 + 14.44 Combine like terms: -4.6 + 14.44 = 9.84 14.44 + -7.6x + x2 = 9.84 Factor a perfect square on the left side: (x + -3.8)(x + -3.8) = 9.84 Calculate the square root of the right side: 3.136877428 Break this problem into two subproblems by setting (x + -3.8) equal to 3.136877428 and -3.136877428.Subproblem 1
x + -3.8 = 3.136877428 Simplifying x + -3.8 = 3.136877428 Reorder the terms: -3.8 + x = 3.136877428 Solving -3.8 + x = 3.136877428 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.8' to each side of the equation. -3.8 + 3.8 + x = 3.136877428 + 3.8 Combine like terms: -3.8 + 3.8 = 0.0 0.0 + x = 3.136877428 + 3.8 x = 3.136877428 + 3.8 Combine like terms: 3.136877428 + 3.8 = 6.936877428 x = 6.936877428 Simplifying x = 6.936877428Subproblem 2
x + -3.8 = -3.136877428 Simplifying x + -3.8 = -3.136877428 Reorder the terms: -3.8 + x = -3.136877428 Solving -3.8 + x = -3.136877428 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.8' to each side of the equation. -3.8 + 3.8 + x = -3.136877428 + 3.8 Combine like terms: -3.8 + 3.8 = 0.0 0.0 + x = -3.136877428 + 3.8 x = -3.136877428 + 3.8 Combine like terms: -3.136877428 + 3.8 = 0.663122572 x = 0.663122572 Simplifying x = 0.663122572Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.936877428, 0.663122572}
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