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Simplifying 2x + -6 + -2x + 12 = (x + 3)(x + -8) Reorder the terms: -6 + 12 + 2x + -2x = (x + 3)(x + -8) Combine like terms: -6 + 12 = 6 6 + 2x + -2x = (x + 3)(x + -8) Combine like terms: 2x + -2x = 0 6 + 0 = (x + 3)(x + -8) 6 = (x + 3)(x + -8) Reorder the terms: 6 = (3 + x)(x + -8) Reorder the terms: 6 = (3 + x)(-8 + x) Multiply (3 + x) * (-8 + x) 6 = (3(-8 + x) + x(-8 + x)) 6 = ((-8 * 3 + x * 3) + x(-8 + x)) 6 = ((-24 + 3x) + x(-8 + x)) 6 = (-24 + 3x + (-8 * x + x * x)) 6 = (-24 + 3x + (-8x + x2)) Combine like terms: 3x + -8x = -5x 6 = (-24 + -5x + x2) Solving 6 = -24 + -5x + x2 Solving for variable 'x'. Combine like terms: 6 + 24 = 30 30 + 5x + -1x2 = -24 + -5x + x2 + 24 + 5x + -1x2 Reorder the terms: 30 + 5x + -1x2 = -24 + 24 + -5x + 5x + x2 + -1x2 Combine like terms: -24 + 24 = 0 30 + 5x + -1x2 = 0 + -5x + 5x + x2 + -1x2 30 + 5x + -1x2 = -5x + 5x + x2 + -1x2 Combine like terms: -5x + 5x = 0 30 + 5x + -1x2 = 0 + x2 + -1x2 30 + 5x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 30 + 5x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -30 + -5x + x2 = 0 Move the constant term to the right: Add '30' to each side of the equation. -30 + -5x + 30 + x2 = 0 + 30 Reorder the terms: -30 + 30 + -5x + x2 = 0 + 30 Combine like terms: -30 + 30 = 0 0 + -5x + x2 = 0 + 30 -5x + x2 = 0 + 30 Combine like terms: 0 + 30 = 30 -5x + x2 = 30 The x term is -5x. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5x + 6.25 + x2 = 30 + 6.25 Reorder the terms: 6.25 + -5x + x2 = 30 + 6.25 Combine like terms: 30 + 6.25 = 36.25 6.25 + -5x + x2 = 36.25 Factor a perfect square on the left side: (x + -2.5)(x + -2.5) = 36.25 Calculate the square root of the right side: 6.020797289 Break this problem into two subproblems by setting (x + -2.5) equal to 6.020797289 and -6.020797289.Subproblem 1
x + -2.5 = 6.020797289 Simplifying x + -2.5 = 6.020797289 Reorder the terms: -2.5 + x = 6.020797289 Solving -2.5 + x = 6.020797289 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = 6.020797289 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = 6.020797289 + 2.5 x = 6.020797289 + 2.5 Combine like terms: 6.020797289 + 2.5 = 8.520797289 x = 8.520797289 Simplifying x = 8.520797289Subproblem 2
x + -2.5 = -6.020797289 Simplifying x + -2.5 = -6.020797289 Reorder the terms: -2.5 + x = -6.020797289 Solving -2.5 + x = -6.020797289 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = -6.020797289 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = -6.020797289 + 2.5 x = -6.020797289 + 2.5 Combine like terms: -6.020797289 + 2.5 = -3.520797289 x = -3.520797289 Simplifying x = -3.520797289Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.520797289, -3.520797289}
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