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Simplifying (x + -2) + -8 + x = x(x + -6) Reorder the terms: (-2 + x) + -8 + x = x(x + -6) Remove parenthesis around (-2 + x) -2 + x + -8 + x = x(x + -6) Reorder the terms: -2 + -8 + x + x = x(x + -6) Combine like terms: -2 + -8 = -10 -10 + x + x = x(x + -6) Combine like terms: x + x = 2x -10 + 2x = x(x + -6) Reorder the terms: -10 + 2x = x(-6 + x) -10 + 2x = (-6 * x + x * x) -10 + 2x = (-6x + x2) Solving -10 + 2x = -6x + x2 Solving for variable 'x'. Combine like terms: 2x + 6x = 8x -10 + 8x + -1x2 = -6x + x2 + 6x + -1x2 Reorder the terms: -10 + 8x + -1x2 = -6x + 6x + x2 + -1x2 Combine like terms: -6x + 6x = 0 -10 + 8x + -1x2 = 0 + x2 + -1x2 -10 + 8x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -10 + 8x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 10 + -8x + x2 = 0 Move the constant term to the right: Add '-10' to each side of the equation. 10 + -8x + -10 + x2 = 0 + -10 Reorder the terms: 10 + -10 + -8x + x2 = 0 + -10 Combine like terms: 10 + -10 = 0 0 + -8x + x2 = 0 + -10 -8x + x2 = 0 + -10 Combine like terms: 0 + -10 = -10 -8x + x2 = -10 The x term is -8x. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8x + 16 + x2 = -10 + 16 Reorder the terms: 16 + -8x + x2 = -10 + 16 Combine like terms: -10 + 16 = 6 16 + -8x + x2 = 6 Factor a perfect square on the left side: (x + -4)(x + -4) = 6 Calculate the square root of the right side: 2.449489743 Break this problem into two subproblems by setting (x + -4) equal to 2.449489743 and -2.449489743.Subproblem 1
x + -4 = 2.449489743 Simplifying x + -4 = 2.449489743 Reorder the terms: -4 + x = 2.449489743 Solving -4 + x = 2.449489743 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = 2.449489743 + 4 Combine like terms: -4 + 4 = 0 0 + x = 2.449489743 + 4 x = 2.449489743 + 4 Combine like terms: 2.449489743 + 4 = 6.449489743 x = 6.449489743 Simplifying x = 6.449489743Subproblem 2
x + -4 = -2.449489743 Simplifying x + -4 = -2.449489743 Reorder the terms: -4 + x = -2.449489743 Solving -4 + x = -2.449489743 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = -2.449489743 + 4 Combine like terms: -4 + 4 = 0 0 + x = -2.449489743 + 4 x = -2.449489743 + 4 Combine like terms: -2.449489743 + 4 = 1.550510257 x = 1.550510257 Simplifying x = 1.550510257Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.449489743, 1.550510257}
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