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Simplifying 42 = (x + -3)(x + -8) Reorder the terms: 42 = (-3 + x)(x + -8) Reorder the terms: 42 = (-3 + x)(-8 + x) Multiply (-3 + x) * (-8 + x) 42 = (-3(-8 + x) + x(-8 + x)) 42 = ((-8 * -3 + x * -3) + x(-8 + x)) 42 = ((24 + -3x) + x(-8 + x)) 42 = (24 + -3x + (-8 * x + x * x)) 42 = (24 + -3x + (-8x + x2)) Combine like terms: -3x + -8x = -11x 42 = (24 + -11x + x2) Solving 42 = 24 + -11x + x2 Solving for variable 'x'. Combine like terms: 42 + -24 = 18 18 + 11x + -1x2 = 24 + -11x + x2 + -24 + 11x + -1x2 Reorder the terms: 18 + 11x + -1x2 = 24 + -24 + -11x + 11x + x2 + -1x2 Combine like terms: 24 + -24 = 0 18 + 11x + -1x2 = 0 + -11x + 11x + x2 + -1x2 18 + 11x + -1x2 = -11x + 11x + x2 + -1x2 Combine like terms: -11x + 11x = 0 18 + 11x + -1x2 = 0 + x2 + -1x2 18 + 11x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 18 + 11x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -18 + -11x + x2 = 0 Move the constant term to the right: Add '18' to each side of the equation. -18 + -11x + 18 + x2 = 0 + 18 Reorder the terms: -18 + 18 + -11x + x2 = 0 + 18 Combine like terms: -18 + 18 = 0 0 + -11x + x2 = 0 + 18 -11x + x2 = 0 + 18 Combine like terms: 0 + 18 = 18 -11x + x2 = 18 The x term is -11x. Take half its coefficient (-5.5). Square it (30.25) and add it to both sides. Add '30.25' to each side of the equation. -11x + 30.25 + x2 = 18 + 30.25 Reorder the terms: 30.25 + -11x + x2 = 18 + 30.25 Combine like terms: 18 + 30.25 = 48.25 30.25 + -11x + x2 = 48.25 Factor a perfect square on the left side: (x + -5.5)(x + -5.5) = 48.25 Calculate the square root of the right side: 6.946221995 Break this problem into two subproblems by setting (x + -5.5) equal to 6.946221995 and -6.946221995.Subproblem 1
x + -5.5 = 6.946221995 Simplifying x + -5.5 = 6.946221995 Reorder the terms: -5.5 + x = 6.946221995 Solving -5.5 + x = 6.946221995 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + x = 6.946221995 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + x = 6.946221995 + 5.5 x = 6.946221995 + 5.5 Combine like terms: 6.946221995 + 5.5 = 12.446221995 x = 12.446221995 Simplifying x = 12.446221995Subproblem 2
x + -5.5 = -6.946221995 Simplifying x + -5.5 = -6.946221995 Reorder the terms: -5.5 + x = -6.946221995 Solving -5.5 + x = -6.946221995 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + x = -6.946221995 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + x = -6.946221995 + 5.5 x = -6.946221995 + 5.5 Combine like terms: -6.946221995 + 5.5 = -1.446221995 x = -1.446221995 Simplifying x = -1.446221995Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.446221995, -1.446221995}
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