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Simplifying 5x + 3x(x + 9) = 107 Reorder the terms: 5x + 3x(9 + x) = 107 5x + (9 * 3x + x * 3x) = 107 5x + (27x + 3x2) = 107 Combine like terms: 5x + 27x = 32x 32x + 3x2 = 107 Solving 32x + 3x2 = 107 Solving for variable 'x'. Reorder the terms: -107 + 32x + 3x2 = 107 + -107 Combine like terms: 107 + -107 = 0 -107 + 32x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -35.66666667 + 10.66666667x + x2 = 0 Move the constant term to the right: Add '35.66666667' to each side of the equation. -35.66666667 + 10.66666667x + 35.66666667 + x2 = 0 + 35.66666667 Reorder the terms: -35.66666667 + 35.66666667 + 10.66666667x + x2 = 0 + 35.66666667 Combine like terms: -35.66666667 + 35.66666667 = 0.00000000 0.00000000 + 10.66666667x + x2 = 0 + 35.66666667 10.66666667x + x2 = 0 + 35.66666667 Combine like terms: 0 + 35.66666667 = 35.66666667 10.66666667x + x2 = 35.66666667 The x term is 10.66666667x. Take half its coefficient (5.333333335). Square it (28.44444446) and add it to both sides. Add '28.44444446' to each side of the equation. 10.66666667x + 28.44444446 + x2 = 35.66666667 + 28.44444446 Reorder the terms: 28.44444446 + 10.66666667x + x2 = 35.66666667 + 28.44444446 Combine like terms: 35.66666667 + 28.44444446 = 64.11111113 28.44444446 + 10.66666667x + x2 = 64.11111113 Factor a perfect square on the left side: (x + 5.333333335)(x + 5.333333335) = 64.11111113 Calculate the square root of the right side: 8.006941434 Break this problem into two subproblems by setting (x + 5.333333335) equal to 8.006941434 and -8.006941434.Subproblem 1
x + 5.333333335 = 8.006941434 Simplifying x + 5.333333335 = 8.006941434 Reorder the terms: 5.333333335 + x = 8.006941434 Solving 5.333333335 + x = 8.006941434 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.333333335' to each side of the equation. 5.333333335 + -5.333333335 + x = 8.006941434 + -5.333333335 Combine like terms: 5.333333335 + -5.333333335 = 0.000000000 0.000000000 + x = 8.006941434 + -5.333333335 x = 8.006941434 + -5.333333335 Combine like terms: 8.006941434 + -5.333333335 = 2.673608099 x = 2.673608099 Simplifying x = 2.673608099Subproblem 2
x + 5.333333335 = -8.006941434 Simplifying x + 5.333333335 = -8.006941434 Reorder the terms: 5.333333335 + x = -8.006941434 Solving 5.333333335 + x = -8.006941434 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.333333335' to each side of the equation. 5.333333335 + -5.333333335 + x = -8.006941434 + -5.333333335 Combine like terms: 5.333333335 + -5.333333335 = 0.000000000 0.000000000 + x = -8.006941434 + -5.333333335 x = -8.006941434 + -5.333333335 Combine like terms: -8.006941434 + -5.333333335 = -13.340274769 x = -13.340274769 Simplifying x = -13.340274769Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.673608099, -13.340274769}
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