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Simplifying 30 + -1x = 3x(x + -6) Reorder the terms: 30 + -1x = 3x(-6 + x) 30 + -1x = (-6 * 3x + x * 3x) 30 + -1x = (-18x + 3x2) Solving 30 + -1x = -18x + 3x2 Solving for variable 'x'. Combine like terms: -1x + 18x = 17x 30 + 17x + -3x2 = -18x + 3x2 + 18x + -3x2 Reorder the terms: 30 + 17x + -3x2 = -18x + 18x + 3x2 + -3x2 Combine like terms: -18x + 18x = 0 30 + 17x + -3x2 = 0 + 3x2 + -3x2 30 + 17x + -3x2 = 3x2 + -3x2 Combine like terms: 3x2 + -3x2 = 0 30 + 17x + -3x2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. -10 + -5.666666667x + x2 = 0 Move the constant term to the right: Add '10' to each side of the equation. -10 + -5.666666667x + 10 + x2 = 0 + 10 Reorder the terms: -10 + 10 + -5.666666667x + x2 = 0 + 10 Combine like terms: -10 + 10 = 0 0 + -5.666666667x + x2 = 0 + 10 -5.666666667x + x2 = 0 + 10 Combine like terms: 0 + 10 = 10 -5.666666667x + x2 = 10 The x term is -5.666666667x. Take half its coefficient (-2.833333334). Square it (8.027777782) and add it to both sides. Add '8.027777782' to each side of the equation. -5.666666667x + 8.027777782 + x2 = 10 + 8.027777782 Reorder the terms: 8.027777782 + -5.666666667x + x2 = 10 + 8.027777782 Combine like terms: 10 + 8.027777782 = 18.027777782 8.027777782 + -5.666666667x + x2 = 18.027777782 Factor a perfect square on the left side: (x + -2.833333334)(x + -2.833333334) = 18.027777782 Calculate the square root of the right side: 4.245913068 Break this problem into two subproblems by setting (x + -2.833333334) equal to 4.245913068 and -4.245913068.Subproblem 1
x + -2.833333334 = 4.245913068 Simplifying x + -2.833333334 = 4.245913068 Reorder the terms: -2.833333334 + x = 4.245913068 Solving -2.833333334 + x = 4.245913068 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.833333334' to each side of the equation. -2.833333334 + 2.833333334 + x = 4.245913068 + 2.833333334 Combine like terms: -2.833333334 + 2.833333334 = 0.000000000 0.000000000 + x = 4.245913068 + 2.833333334 x = 4.245913068 + 2.833333334 Combine like terms: 4.245913068 + 2.833333334 = 7.079246402 x = 7.079246402 Simplifying x = 7.079246402Subproblem 2
x + -2.833333334 = -4.245913068 Simplifying x + -2.833333334 = -4.245913068 Reorder the terms: -2.833333334 + x = -4.245913068 Solving -2.833333334 + x = -4.245913068 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.833333334' to each side of the equation. -2.833333334 + 2.833333334 + x = -4.245913068 + 2.833333334 Combine like terms: -2.833333334 + 2.833333334 = 0.000000000 0.000000000 + x = -4.245913068 + 2.833333334 x = -4.245913068 + 2.833333334 Combine like terms: -4.245913068 + 2.833333334 = -1.412579734 x = -1.412579734 Simplifying x = -1.412579734Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.079246402, -1.412579734}
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