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Simplifying (x + -9)(x + -3) = (x + 1) Reorder the terms: (-9 + x)(x + -3) = (x + 1) Reorder the terms: (-9 + x)(-3 + x) = (x + 1) Multiply (-9 + x) * (-3 + x) (-9(-3 + x) + x(-3 + x)) = (x + 1) ((-3 * -9 + x * -9) + x(-3 + x)) = (x + 1) ((27 + -9x) + x(-3 + x)) = (x + 1) (27 + -9x + (-3 * x + x * x)) = (x + 1) (27 + -9x + (-3x + x2)) = (x + 1) Combine like terms: -9x + -3x = -12x (27 + -12x + x2) = (x + 1) Reorder the terms: 27 + -12x + x2 = (1 + x) Remove parenthesis around (1 + x) 27 + -12x + x2 = 1 + x Solving 27 + -12x + x2 = 1 + x Solving for variable 'x'. Reorder the terms: 27 + -1 + -12x + -1x + x2 = 1 + x + -1 + -1x Combine like terms: 27 + -1 = 26 26 + -12x + -1x + x2 = 1 + x + -1 + -1x Combine like terms: -12x + -1x = -13x 26 + -13x + x2 = 1 + x + -1 + -1x Reorder the terms: 26 + -13x + x2 = 1 + -1 + x + -1x Combine like terms: 1 + -1 = 0 26 + -13x + x2 = 0 + x + -1x 26 + -13x + x2 = x + -1x Combine like terms: x + -1x = 0 26 + -13x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-26' to each side of the equation. 26 + -13x + -26 + x2 = 0 + -26 Reorder the terms: 26 + -26 + -13x + x2 = 0 + -26 Combine like terms: 26 + -26 = 0 0 + -13x + x2 = 0 + -26 -13x + x2 = 0 + -26 Combine like terms: 0 + -26 = -26 -13x + x2 = -26 The x term is -13x. Take half its coefficient (-6.5). Square it (42.25) and add it to both sides. Add '42.25' to each side of the equation. -13x + 42.25 + x2 = -26 + 42.25 Reorder the terms: 42.25 + -13x + x2 = -26 + 42.25 Combine like terms: -26 + 42.25 = 16.25 42.25 + -13x + x2 = 16.25 Factor a perfect square on the left side: (x + -6.5)(x + -6.5) = 16.25 Calculate the square root of the right side: 4.031128874 Break this problem into two subproblems by setting (x + -6.5) equal to 4.031128874 and -4.031128874.Subproblem 1
x + -6.5 = 4.031128874 Simplifying x + -6.5 = 4.031128874 Reorder the terms: -6.5 + x = 4.031128874 Solving -6.5 + x = 4.031128874 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.5' to each side of the equation. -6.5 + 6.5 + x = 4.031128874 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + x = 4.031128874 + 6.5 x = 4.031128874 + 6.5 Combine like terms: 4.031128874 + 6.5 = 10.531128874 x = 10.531128874 Simplifying x = 10.531128874Subproblem 2
x + -6.5 = -4.031128874 Simplifying x + -6.5 = -4.031128874 Reorder the terms: -6.5 + x = -4.031128874 Solving -6.5 + x = -4.031128874 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.5' to each side of the equation. -6.5 + 6.5 + x = -4.031128874 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + x = -4.031128874 + 6.5 x = -4.031128874 + 6.5 Combine like terms: -4.031128874 + 6.5 = 2.468871126 x = 2.468871126 Simplifying x = 2.468871126Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.531128874, 2.468871126}
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