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Simplifying 3x2 + 9 = 11x Reorder the terms: 9 + 3x2 = 11x Solving 9 + 3x2 = 11x Solving for variable 'x'. Reorder the terms: 9 + -11x + 3x2 = 11x + -11x Combine like terms: 11x + -11x = 0 9 + -11x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 3 + -3.666666667x + x2 = 0 Move the constant term to the right: Add '-3' to each side of the equation. 3 + -3.666666667x + -3 + x2 = 0 + -3 Reorder the terms: 3 + -3 + -3.666666667x + x2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -3.666666667x + x2 = 0 + -3 -3.666666667x + x2 = 0 + -3 Combine like terms: 0 + -3 = -3 -3.666666667x + x2 = -3 The x term is -3.666666667x. Take half its coefficient (-1.833333334). Square it (3.361111114) and add it to both sides. Add '3.361111114' to each side of the equation. -3.666666667x + 3.361111114 + x2 = -3 + 3.361111114 Reorder the terms: 3.361111114 + -3.666666667x + x2 = -3 + 3.361111114 Combine like terms: -3 + 3.361111114 = 0.361111114 3.361111114 + -3.666666667x + x2 = 0.361111114 Factor a perfect square on the left side: (x + -1.833333334)(x + -1.833333334) = 0.361111114 Calculate the square root of the right side: 0.600925215 Break this problem into two subproblems by setting (x + -1.833333334) equal to 0.600925215 and -0.600925215.Subproblem 1
x + -1.833333334 = 0.600925215 Simplifying x + -1.833333334 = 0.600925215 Reorder the terms: -1.833333334 + x = 0.600925215 Solving -1.833333334 + x = 0.600925215 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.833333334' to each side of the equation. -1.833333334 + 1.833333334 + x = 0.600925215 + 1.833333334 Combine like terms: -1.833333334 + 1.833333334 = 0.000000000 0.000000000 + x = 0.600925215 + 1.833333334 x = 0.600925215 + 1.833333334 Combine like terms: 0.600925215 + 1.833333334 = 2.434258549 x = 2.434258549 Simplifying x = 2.434258549Subproblem 2
x + -1.833333334 = -0.600925215 Simplifying x + -1.833333334 = -0.600925215 Reorder the terms: -1.833333334 + x = -0.600925215 Solving -1.833333334 + x = -0.600925215 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.833333334' to each side of the equation. -1.833333334 + 1.833333334 + x = -0.600925215 + 1.833333334 Combine like terms: -1.833333334 + 1.833333334 = 0.000000000 0.000000000 + x = -0.600925215 + 1.833333334 x = -0.600925215 + 1.833333334 Combine like terms: -0.600925215 + 1.833333334 = 1.232408119 x = 1.232408119 Simplifying x = 1.232408119Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.434258549, 1.232408119}
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