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Simplifying 6x(x + -3) + -8 = 16x + -7 Reorder the terms: 6x(-3 + x) + -8 = 16x + -7 (-3 * 6x + x * 6x) + -8 = 16x + -7 (-18x + 6x2) + -8 = 16x + -7 Reorder the terms: -8 + -18x + 6x2 = 16x + -7 Reorder the terms: -8 + -18x + 6x2 = -7 + 16x Solving -8 + -18x + 6x2 = -7 + 16x Solving for variable 'x'. Reorder the terms: -8 + 7 + -18x + -16x + 6x2 = -7 + 16x + 7 + -16x Combine like terms: -8 + 7 = -1 -1 + -18x + -16x + 6x2 = -7 + 16x + 7 + -16x Combine like terms: -18x + -16x = -34x -1 + -34x + 6x2 = -7 + 16x + 7 + -16x Reorder the terms: -1 + -34x + 6x2 = -7 + 7 + 16x + -16x Combine like terms: -7 + 7 = 0 -1 + -34x + 6x2 = 0 + 16x + -16x -1 + -34x + 6x2 = 16x + -16x Combine like terms: 16x + -16x = 0 -1 + -34x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -0.1666666667 + -5.666666667x + x2 = 0 Move the constant term to the right: Add '0.1666666667' to each side of the equation. -0.1666666667 + -5.666666667x + 0.1666666667 + x2 = 0 + 0.1666666667 Reorder the terms: -0.1666666667 + 0.1666666667 + -5.666666667x + x2 = 0 + 0.1666666667 Combine like terms: -0.1666666667 + 0.1666666667 = 0.0000000000 0.0000000000 + -5.666666667x + x2 = 0 + 0.1666666667 -5.666666667x + x2 = 0 + 0.1666666667 Combine like terms: 0 + 0.1666666667 = 0.1666666667 -5.666666667x + x2 = 0.1666666667 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 = 0.1666666667 + 8.027777782 Reorder the terms: 8.027777782 + -5.666666667x + x2 = 0.1666666667 + 8.027777782 Combine like terms: 0.1666666667 + 8.027777782 = 8.1944444487 8.027777782 + -5.666666667x + x2 = 8.1944444487 Factor a perfect square on the left side: (x + -2.833333334)(x + -2.833333334) = 8.1944444487 Calculate the square root of the right side: 2.862594007 Break this problem into two subproblems by setting (x + -2.833333334) equal to 2.862594007 and -2.862594007.Subproblem 1
x + -2.833333334 = 2.862594007 Simplifying x + -2.833333334 = 2.862594007 Reorder the terms: -2.833333334 + x = 2.862594007 Solving -2.833333334 + x = 2.862594007 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 = 2.862594007 + 2.833333334 Combine like terms: -2.833333334 + 2.833333334 = 0.000000000 0.000000000 + x = 2.862594007 + 2.833333334 x = 2.862594007 + 2.833333334 Combine like terms: 2.862594007 + 2.833333334 = 5.695927341 x = 5.695927341 Simplifying x = 5.695927341Subproblem 2
x + -2.833333334 = -2.862594007 Simplifying x + -2.833333334 = -2.862594007 Reorder the terms: -2.833333334 + x = -2.862594007 Solving -2.833333334 + x = -2.862594007 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 = -2.862594007 + 2.833333334 Combine like terms: -2.833333334 + 2.833333334 = 0.000000000 0.000000000 + x = -2.862594007 + 2.833333334 x = -2.862594007 + 2.833333334 Combine like terms: -2.862594007 + 2.833333334 = -0.029260673 x = -0.029260673 Simplifying x = -0.029260673Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.695927341, -0.029260673}
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