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Simplifying 2x2 + 6x + -4 + -1(x + 1)(x + 1) = 0 Reorder the terms: 2x2 + 6x + -4 + -1(1 + x)(x + 1) = 0 Reorder the terms: 2x2 + 6x + -4 + -1(1 + x)(1 + x) = 0 Multiply (1 + x) * (1 + x) 2x2 + 6x + -4 + -1(1(1 + x) + x(1 + x)) = 0 2x2 + 6x + -4 + -1((1 * 1 + x * 1) + x(1 + x)) = 0 2x2 + 6x + -4 + -1((1 + 1x) + x(1 + x)) = 0 2x2 + 6x + -4 + -1(1 + 1x + (1 * x + x * x)) = 0 2x2 + 6x + -4 + -1(1 + 1x + (1x + x2)) = 0 Combine like terms: 1x + 1x = 2x 2x2 + 6x + -4 + -1(1 + 2x + x2) = 0 2x2 + 6x + -4 + (1 * -1 + 2x * -1 + x2 * -1) = 0 2x2 + 6x + -4 + (-1 + -2x + -1x2) = 0 Reorder the terms: -4 + -1 + 6x + -2x + 2x2 + -1x2 = 0 Combine like terms: -4 + -1 = -5 -5 + 6x + -2x + 2x2 + -1x2 = 0 Combine like terms: 6x + -2x = 4x -5 + 4x + 2x2 + -1x2 = 0 Combine like terms: 2x2 + -1x2 = 1x2 -5 + 4x + 1x2 = 0 Solving -5 + 4x + 1x2 = 0 Solving for variable 'x'. Factor a trinomial. (-5 + -1x)(1 + -1x) = 0Subproblem 1
Set the factor '(-5 + -1x)' equal to zero and attempt to solve: Simplifying -5 + -1x = 0 Solving -5 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + -1x = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -1x = 0 + 5 -1x = 0 + 5 Combine like terms: 0 + 5 = 5 -1x = 5 Divide each side by '-1'. x = -5 Simplifying x = -5Subproblem 2
Set the factor '(1 + -1x)' equal to zero and attempt to solve: Simplifying 1 + -1x = 0 Solving 1 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -1x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1x = 0 + -1 -1x = 0 + -1 Combine like terms: 0 + -1 = -1 -1x = -1 Divide each side by '-1'. x = 1 Simplifying x = 1Solution
x = {-5, 1}
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