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Simplifying (x + -4)(x + -2) + 1 = 0 Reorder the terms: (-4 + x)(x + -2) + 1 = 0 Reorder the terms: (-4 + x)(-2 + x) + 1 = 0 Multiply (-4 + x) * (-2 + x) (-4(-2 + x) + x(-2 + x)) + 1 = 0 ((-2 * -4 + x * -4) + x(-2 + x)) + 1 = 0 ((8 + -4x) + x(-2 + x)) + 1 = 0 (8 + -4x + (-2 * x + x * x)) + 1 = 0 (8 + -4x + (-2x + x2)) + 1 = 0 Combine like terms: -4x + -2x = -6x (8 + -6x + x2) + 1 = 0 Reorder the terms: 8 + 1 + -6x + x2 = 0 Combine like terms: 8 + 1 = 9 9 + -6x + x2 = 0 Solving 9 + -6x + x2 = 0 Solving for variable 'x'. Factor a trinomial. (3 + -1x)(3 + -1x) = 0Subproblem 1
Set the factor '(3 + -1x)' equal to zero and attempt to solve: Simplifying 3 + -1x = 0 Solving 3 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -1x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1x = 0 + -3 -1x = 0 + -3 Combine like terms: 0 + -3 = -3 -1x = -3 Divide each side by '-1'. x = 3 Simplifying x = 3Subproblem 2
Set the factor '(3 + -1x)' equal to zero and attempt to solve: Simplifying 3 + -1x = 0 Solving 3 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -1x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1x = 0 + -3 -1x = 0 + -3 Combine like terms: 0 + -3 = -3 -1x = -3 Divide each side by '-1'. x = 3 Simplifying x = 3Solution
x = {3, 3}
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