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Simplifying x = 2(x + -3)(x + -8) Reorder the terms: x = 2(-3 + x)(x + -8) Reorder the terms: x = 2(-3 + x)(-8 + x) Multiply (-3 + x) * (-8 + x) x = 2(-3(-8 + x) + x(-8 + x)) x = 2((-8 * -3 + x * -3) + x(-8 + x)) x = 2((24 + -3x) + x(-8 + x)) x = 2(24 + -3x + (-8 * x + x * x)) x = 2(24 + -3x + (-8x + x2)) Combine like terms: -3x + -8x = -11x x = 2(24 + -11x + x2) x = (24 * 2 + -11x * 2 + x2 * 2) x = (48 + -22x + 2x2) Solving x = 48 + -22x + 2x2 Solving for variable 'x'. Reorder the terms: -48 + x + 22x + -2x2 = 48 + -22x + 2x2 + -48 + 22x + -2x2 Combine like terms: x + 22x = 23x -48 + 23x + -2x2 = 48 + -22x + 2x2 + -48 + 22x + -2x2 Reorder the terms: -48 + 23x + -2x2 = 48 + -48 + -22x + 22x + 2x2 + -2x2 Combine like terms: 48 + -48 = 0 -48 + 23x + -2x2 = 0 + -22x + 22x + 2x2 + -2x2 -48 + 23x + -2x2 = -22x + 22x + 2x2 + -2x2 Combine like terms: -22x + 22x = 0 -48 + 23x + -2x2 = 0 + 2x2 + -2x2 -48 + 23x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 -48 + 23x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. 24 + -11.5x + x2 = 0 Move the constant term to the right: Add '-24' to each side of the equation. 24 + -11.5x + -24 + x2 = 0 + -24 Reorder the terms: 24 + -24 + -11.5x + x2 = 0 + -24 Combine like terms: 24 + -24 = 0 0 + -11.5x + x2 = 0 + -24 -11.5x + x2 = 0 + -24 Combine like terms: 0 + -24 = -24 -11.5x + x2 = -24 The x term is -11.5x. Take half its coefficient (-5.75). Square it (33.0625) and add it to both sides. Add '33.0625' to each side of the equation. -11.5x + 33.0625 + x2 = -24 + 33.0625 Reorder the terms: 33.0625 + -11.5x + x2 = -24 + 33.0625 Combine like terms: -24 + 33.0625 = 9.0625 33.0625 + -11.5x + x2 = 9.0625 Factor a perfect square on the left side: (x + -5.75)(x + -5.75) = 9.0625 Calculate the square root of the right side: 3.010398645 Break this problem into two subproblems by setting (x + -5.75) equal to 3.010398645 and -3.010398645.Subproblem 1
x + -5.75 = 3.010398645 Simplifying x + -5.75 = 3.010398645 Reorder the terms: -5.75 + x = 3.010398645 Solving -5.75 + x = 3.010398645 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.75' to each side of the equation. -5.75 + 5.75 + x = 3.010398645 + 5.75 Combine like terms: -5.75 + 5.75 = 0.00 0.00 + x = 3.010398645 + 5.75 x = 3.010398645 + 5.75 Combine like terms: 3.010398645 + 5.75 = 8.760398645 x = 8.760398645 Simplifying x = 8.760398645Subproblem 2
x + -5.75 = -3.010398645 Simplifying x + -5.75 = -3.010398645 Reorder the terms: -5.75 + x = -3.010398645 Solving -5.75 + x = -3.010398645 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.75' to each side of the equation. -5.75 + 5.75 + x = -3.010398645 + 5.75 Combine like terms: -5.75 + 5.75 = 0.00 0.00 + x = -3.010398645 + 5.75 x = -3.010398645 + 5.75 Combine like terms: -3.010398645 + 5.75 = 2.739601355 x = 2.739601355 Simplifying x = 2.739601355Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.760398645, 2.739601355}
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