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Simplifying 3x(x + -8) + x = 16 Reorder the terms: 3x(-8 + x) + x = 16 (-8 * 3x + x * 3x) + x = 16 (-24x + 3x2) + x = 16 Reorder the terms: -24x + x + 3x2 = 16 Combine like terms: -24x + x = -23x -23x + 3x2 = 16 Solving -23x + 3x2 = 16 Solving for variable 'x'. Reorder the terms: -16 + -23x + 3x2 = 16 + -16 Combine like terms: 16 + -16 = 0 -16 + -23x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -5.333333333 + -7.666666667x + x2 = 0 Move the constant term to the right: Add '5.333333333' to each side of the equation. -5.333333333 + -7.666666667x + 5.333333333 + x2 = 0 + 5.333333333 Reorder the terms: -5.333333333 + 5.333333333 + -7.666666667x + x2 = 0 + 5.333333333 Combine like terms: -5.333333333 + 5.333333333 = 0.000000000 0.000000000 + -7.666666667x + x2 = 0 + 5.333333333 -7.666666667x + x2 = 0 + 5.333333333 Combine like terms: 0 + 5.333333333 = 5.333333333 -7.666666667x + x2 = 5.333333333 The x term is -7.666666667x. Take half its coefficient (-3.833333334). Square it (14.69444445) and add it to both sides. Add '14.69444445' to each side of the equation. -7.666666667x + 14.69444445 + x2 = 5.333333333 + 14.69444445 Reorder the terms: 14.69444445 + -7.666666667x + x2 = 5.333333333 + 14.69444445 Combine like terms: 5.333333333 + 14.69444445 = 20.027777783 14.69444445 + -7.666666667x + x2 = 20.027777783 Factor a perfect square on the left side: (x + -3.833333334)(x + -3.833333334) = 20.027777783 Calculate the square root of the right side: 4.475240528 Break this problem into two subproblems by setting (x + -3.833333334) equal to 4.475240528 and -4.475240528.Subproblem 1
x + -3.833333334 = 4.475240528 Simplifying x + -3.833333334 = 4.475240528 Reorder the terms: -3.833333334 + x = 4.475240528 Solving -3.833333334 + x = 4.475240528 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.833333334' to each side of the equation. -3.833333334 + 3.833333334 + x = 4.475240528 + 3.833333334 Combine like terms: -3.833333334 + 3.833333334 = 0.000000000 0.000000000 + x = 4.475240528 + 3.833333334 x = 4.475240528 + 3.833333334 Combine like terms: 4.475240528 + 3.833333334 = 8.308573862 x = 8.308573862 Simplifying x = 8.308573862Subproblem 2
x + -3.833333334 = -4.475240528 Simplifying x + -3.833333334 = -4.475240528 Reorder the terms: -3.833333334 + x = -4.475240528 Solving -3.833333334 + x = -4.475240528 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.833333334' to each side of the equation. -3.833333334 + 3.833333334 + x = -4.475240528 + 3.833333334 Combine like terms: -3.833333334 + 3.833333334 = 0.000000000 0.000000000 + x = -4.475240528 + 3.833333334 x = -4.475240528 + 3.833333334 Combine like terms: -4.475240528 + 3.833333334 = -0.641907194 x = -0.641907194 Simplifying x = -0.641907194Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.308573862, -0.641907194}
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