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Simplifying 3x2 + -47x + -18 = 0 Reorder the terms: -18 + -47x + 3x2 = 0 Solving -18 + -47x + 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 + -15.66666667x + x2 = 0 Move the constant term to the right: Add '6' to each side of the equation. -6 + -15.66666667x + 6 + x2 = 0 + 6 Reorder the terms: -6 + 6 + -15.66666667x + x2 = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -15.66666667x + x2 = 0 + 6 -15.66666667x + x2 = 0 + 6 Combine like terms: 0 + 6 = 6 -15.66666667x + x2 = 6 The x term is -15.66666667x. Take half its coefficient (-7.833333335). Square it (61.36111114) and add it to both sides. Add '61.36111114' to each side of the equation. -15.66666667x + 61.36111114 + x2 = 6 + 61.36111114 Reorder the terms: 61.36111114 + -15.66666667x + x2 = 6 + 61.36111114 Combine like terms: 6 + 61.36111114 = 67.36111114 61.36111114 + -15.66666667x + x2 = 67.36111114 Factor a perfect square on the left side: (x + -7.833333335)(x + -7.833333335) = 67.36111114 Calculate the square root of the right side: 8.207381503 Break this problem into two subproblems by setting (x + -7.833333335) equal to 8.207381503 and -8.207381503.Subproblem 1
x + -7.833333335 = 8.207381503 Simplifying x + -7.833333335 = 8.207381503 Reorder the terms: -7.833333335 + x = 8.207381503 Solving -7.833333335 + x = 8.207381503 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.833333335' to each side of the equation. -7.833333335 + 7.833333335 + x = 8.207381503 + 7.833333335 Combine like terms: -7.833333335 + 7.833333335 = 0.000000000 0.000000000 + x = 8.207381503 + 7.833333335 x = 8.207381503 + 7.833333335 Combine like terms: 8.207381503 + 7.833333335 = 16.040714838 x = 16.040714838 Simplifying x = 16.040714838Subproblem 2
x + -7.833333335 = -8.207381503 Simplifying x + -7.833333335 = -8.207381503 Reorder the terms: -7.833333335 + x = -8.207381503 Solving -7.833333335 + x = -8.207381503 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.833333335' to each side of the equation. -7.833333335 + 7.833333335 + x = -8.207381503 + 7.833333335 Combine like terms: -7.833333335 + 7.833333335 = 0.000000000 0.000000000 + x = -8.207381503 + 7.833333335 x = -8.207381503 + 7.833333335 Combine like terms: -8.207381503 + 7.833333335 = -0.374048168 x = -0.374048168 Simplifying x = -0.374048168Solution
The solution to the problem is based on the solutions from the subproblems. x = {16.040714838, -0.374048168}
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