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Simplifying 6x2 + -25x + 23 = 0 Reorder the terms: 23 + -25x + 6x2 = 0 Solving 23 + -25x + 6x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. 3.833333333 + -4.166666667x + x2 = 0 Move the constant term to the right: Add '-3.833333333' to each side of the equation. 3.833333333 + -4.166666667x + -3.833333333 + x2 = 0 + -3.833333333 Reorder the terms: 3.833333333 + -3.833333333 + -4.166666667x + x2 = 0 + -3.833333333 Combine like terms: 3.833333333 + -3.833333333 = 0.000000000 0.000000000 + -4.166666667x + x2 = 0 + -3.833333333 -4.166666667x + x2 = 0 + -3.833333333 Combine like terms: 0 + -3.833333333 = -3.833333333 -4.166666667x + x2 = -3.833333333 The x term is -4.166666667x. Take half its coefficient (-2.083333334). Square it (4.340277781) and add it to both sides. Add '4.340277781' to each side of the equation. -4.166666667x + 4.340277781 + x2 = -3.833333333 + 4.340277781 Reorder the terms: 4.340277781 + -4.166666667x + x2 = -3.833333333 + 4.340277781 Combine like terms: -3.833333333 + 4.340277781 = 0.506944448 4.340277781 + -4.166666667x + x2 = 0.506944448 Factor a perfect square on the left side: (x + -2.083333334)(x + -2.083333334) = 0.506944448 Calculate the square root of the right side: 0.712000315 Break this problem into two subproblems by setting (x + -2.083333334) equal to 0.712000315 and -0.712000315.Subproblem 1
x + -2.083333334 = 0.712000315 Simplifying x + -2.083333334 = 0.712000315 Reorder the terms: -2.083333334 + x = 0.712000315 Solving -2.083333334 + x = 0.712000315 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.083333334' to each side of the equation. -2.083333334 + 2.083333334 + x = 0.712000315 + 2.083333334 Combine like terms: -2.083333334 + 2.083333334 = 0.000000000 0.000000000 + x = 0.712000315 + 2.083333334 x = 0.712000315 + 2.083333334 Combine like terms: 0.712000315 + 2.083333334 = 2.795333649 x = 2.795333649 Simplifying x = 2.795333649Subproblem 2
x + -2.083333334 = -0.712000315 Simplifying x + -2.083333334 = -0.712000315 Reorder the terms: -2.083333334 + x = -0.712000315 Solving -2.083333334 + x = -0.712000315 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.083333334' to each side of the equation. -2.083333334 + 2.083333334 + x = -0.712000315 + 2.083333334 Combine like terms: -2.083333334 + 2.083333334 = 0.000000000 0.000000000 + x = -0.712000315 + 2.083333334 x = -0.712000315 + 2.083333334 Combine like terms: -0.712000315 + 2.083333334 = 1.371333019 x = 1.371333019 Simplifying x = 1.371333019Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.795333649, 1.371333019}
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