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Simplifying 3x2 + 23x + -108 = 0 Reorder the terms: -108 + 23x + 3x2 = 0 Solving -108 + 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'. -36 + 7.666666667x + x2 = 0 Move the constant term to the right: Add '36' to each side of the equation. -36 + 7.666666667x + 36 + x2 = 0 + 36 Reorder the terms: -36 + 36 + 7.666666667x + x2 = 0 + 36 Combine like terms: -36 + 36 = 0 0 + 7.666666667x + x2 = 0 + 36 7.666666667x + x2 = 0 + 36 Combine like terms: 0 + 36 = 36 7.666666667x + x2 = 36 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 = 36 + 14.69444445 Reorder the terms: 14.69444445 + 7.666666667x + x2 = 36 + 14.69444445 Combine like terms: 36 + 14.69444445 = 50.69444445 14.69444445 + 7.666666667x + x2 = 50.69444445 Factor a perfect square on the left side: (x + 3.833333334)(x + 3.833333334) = 50.69444445 Calculate the square root of the right side: 7.120003121 Break this problem into two subproblems by setting (x + 3.833333334) equal to 7.120003121 and -7.120003121.Subproblem 1
x + 3.833333334 = 7.120003121 Simplifying x + 3.833333334 = 7.120003121 Reorder the terms: 3.833333334 + x = 7.120003121 Solving 3.833333334 + x = 7.120003121 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 = 7.120003121 + -3.833333334 Combine like terms: 3.833333334 + -3.833333334 = 0.000000000 0.000000000 + x = 7.120003121 + -3.833333334 x = 7.120003121 + -3.833333334 Combine like terms: 7.120003121 + -3.833333334 = 3.286669787 x = 3.286669787 Simplifying x = 3.286669787Subproblem 2
x + 3.833333334 = -7.120003121 Simplifying x + 3.833333334 = -7.120003121 Reorder the terms: 3.833333334 + x = -7.120003121 Solving 3.833333334 + x = -7.120003121 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 = -7.120003121 + -3.833333334 Combine like terms: 3.833333334 + -3.833333334 = 0.000000000 0.000000000 + x = -7.120003121 + -3.833333334 x = -7.120003121 + -3.833333334 Combine like terms: -7.120003121 + -3.833333334 = -10.953336455 x = -10.953336455 Simplifying x = -10.953336455Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.286669787, -10.953336455}
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