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Simplifying 3x2 + 23x + -18 = 0 Reorder the terms: -18 + 23x + 3x2 = 0 Solving -18 + 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'. -6 + 7.666666667x + x2 = 0 Move the constant term to the right: Add '6' to each side of the equation. -6 + 7.666666667x + 6 + x2 = 0 + 6 Reorder the terms: -6 + 6 + 7.666666667x + x2 = 0 + 6 Combine like terms: -6 + 6 = 0 0 + 7.666666667x + x2 = 0 + 6 7.666666667x + x2 = 0 + 6 Combine like terms: 0 + 6 = 6 7.666666667x + x2 = 6 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 = 6 + 14.69444445 Reorder the terms: 14.69444445 + 7.666666667x + x2 = 6 + 14.69444445 Combine like terms: 6 + 14.69444445 = 20.69444445 14.69444445 + 7.666666667x + x2 = 20.69444445 Factor a perfect square on the left side: (x + 3.833333334)(x + 3.833333334) = 20.69444445 Calculate the square root of the right side: 4.549114689 Break this problem into two subproblems by setting (x + 3.833333334) equal to 4.549114689 and -4.549114689.Subproblem 1
x + 3.833333334 = 4.549114689 Simplifying x + 3.833333334 = 4.549114689 Reorder the terms: 3.833333334 + x = 4.549114689 Solving 3.833333334 + x = 4.549114689 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 = 4.549114689 + -3.833333334 Combine like terms: 3.833333334 + -3.833333334 = 0.000000000 0.000000000 + x = 4.549114689 + -3.833333334 x = 4.549114689 + -3.833333334 Combine like terms: 4.549114689 + -3.833333334 = 0.715781355 x = 0.715781355 Simplifying x = 0.715781355Subproblem 2
x + 3.833333334 = -4.549114689 Simplifying x + 3.833333334 = -4.549114689 Reorder the terms: 3.833333334 + x = -4.549114689 Solving 3.833333334 + x = -4.549114689 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 = -4.549114689 + -3.833333334 Combine like terms: 3.833333334 + -3.833333334 = 0.000000000 0.000000000 + x = -4.549114689 + -3.833333334 x = -4.549114689 + -3.833333334 Combine like terms: -4.549114689 + -3.833333334 = -8.382448023 x = -8.382448023 Simplifying x = -8.382448023Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.715781355, -8.382448023}
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