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Simplifying 3x2 + 23x + -6 = 0 Reorder the terms: -6 + 23x + 3x2 = 0 Solving -6 + 23x + 3x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -2 + 7.666666667x + x2 = 0 Move the constant term to the right: Add '2' to each side of the equation. -2 + 7.666666667x + 2 + x2 = 0 + 2 Reorder the terms: -2 + 2 + 7.666666667x + x2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + 7.666666667x + x2 = 0 + 2 7.666666667x + x2 = 0 + 2 Combine like terms: 0 + 2 = 2 7.666666667x + x2 = 2 The x term is 7.666666667x. Take half its coefficient (3.833333334). Square it (14.69444445) and add it to both sides. Add '14.69444445' to each side of the equation. 7.666666667x + 14.69444445 + x2 = 2 + 14.69444445 Reorder the terms: 14.69444445 + 7.666666667x + x2 = 2 + 14.69444445 Combine like terms: 2 + 14.69444445 = 16.69444445 14.69444445 + 7.666666667x + x2 = 16.69444445 Factor a perfect square on the left side: (x + 3.833333334)(x + 3.833333334) = 16.69444445 Calculate the square root of the right side: 4.085883558 Break this problem into two subproblems by setting (x + 3.833333334) equal to 4.085883558 and -4.085883558.Subproblem 1
x + 3.833333334 = 4.085883558 Simplifying x + 3.833333334 = 4.085883558 Reorder the terms: 3.833333334 + x = 4.085883558 Solving 3.833333334 + x = 4.085883558 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.833333334' to each side of the equation. 3.833333334 + -3.833333334 + x = 4.085883558 + -3.833333334 Combine like terms: 3.833333334 + -3.833333334 = 0.000000000 0.000000000 + x = 4.085883558 + -3.833333334 x = 4.085883558 + -3.833333334 Combine like terms: 4.085883558 + -3.833333334 = 0.252550224 x = 0.252550224 Simplifying x = 0.252550224Subproblem 2
x + 3.833333334 = -4.085883558 Simplifying x + 3.833333334 = -4.085883558 Reorder the terms: 3.833333334 + x = -4.085883558 Solving 3.833333334 + x = -4.085883558 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.833333334' to each side of the equation. 3.833333334 + -3.833333334 + x = -4.085883558 + -3.833333334 Combine like terms: 3.833333334 + -3.833333334 = 0.000000000 0.000000000 + x = -4.085883558 + -3.833333334 x = -4.085883558 + -3.833333334 Combine like terms: -4.085883558 + -3.833333334 = -7.919216892 x = -7.919216892 Simplifying x = -7.919216892Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.252550224, -7.919216892}
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