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Simplifying 3.8x2 + -25x + 23 = 0 Reorder the terms: 23 + -25x + 3.8x2 = 0 Solving 23 + -25x + 3.8x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 3.8 the coefficient of the squared term: Divide each side by '3.8'. 6.052631579 + -6.578947368x + x2 = 0 Move the constant term to the right: Add '-6.052631579' to each side of the equation. 6.052631579 + -6.578947368x + -6.052631579 + x2 = 0 + -6.052631579 Reorder the terms: 6.052631579 + -6.052631579 + -6.578947368x + x2 = 0 + -6.052631579 Combine like terms: 6.052631579 + -6.052631579 = 0.000000000 0.000000000 + -6.578947368x + x2 = 0 + -6.052631579 -6.578947368x + x2 = 0 + -6.052631579 Combine like terms: 0 + -6.052631579 = -6.052631579 -6.578947368x + x2 = -6.052631579 The x term is -6.578947368x. Take half its coefficient (-3.289473684). Square it (10.82063712) and add it to both sides. Add '10.82063712' to each side of the equation. -6.578947368x + 10.82063712 + x2 = -6.052631579 + 10.82063712 Reorder the terms: 10.82063712 + -6.578947368x + x2 = -6.052631579 + 10.82063712 Combine like terms: -6.052631579 + 10.82063712 = 4.768005541 10.82063712 + -6.578947368x + x2 = 4.768005541 Factor a perfect square on the left side: (x + -3.289473684)(x + -3.289473684) = 4.768005541 Calculate the square root of the right side: 2.183576319 Break this problem into two subproblems by setting (x + -3.289473684) equal to 2.183576319 and -2.183576319.Subproblem 1
x + -3.289473684 = 2.183576319 Simplifying x + -3.289473684 = 2.183576319 Reorder the terms: -3.289473684 + x = 2.183576319 Solving -3.289473684 + x = 2.183576319 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.289473684' to each side of the equation. -3.289473684 + 3.289473684 + x = 2.183576319 + 3.289473684 Combine like terms: -3.289473684 + 3.289473684 = 0.000000000 0.000000000 + x = 2.183576319 + 3.289473684 x = 2.183576319 + 3.289473684 Combine like terms: 2.183576319 + 3.289473684 = 5.473050003 x = 5.473050003 Simplifying x = 5.473050003Subproblem 2
x + -3.289473684 = -2.183576319 Simplifying x + -3.289473684 = -2.183576319 Reorder the terms: -3.289473684 + x = -2.183576319 Solving -3.289473684 + x = -2.183576319 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.289473684' to each side of the equation. -3.289473684 + 3.289473684 + x = -2.183576319 + 3.289473684 Combine like terms: -3.289473684 + 3.289473684 = 0.000000000 0.000000000 + x = -2.183576319 + 3.289473684 x = -2.183576319 + 3.289473684 Combine like terms: -2.183576319 + 3.289473684 = 1.105897365 x = 1.105897365 Simplifying x = 1.105897365Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.473050003, 1.105897365}
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