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Simplifying (4x2 + -3) + -1(x2 + x + 1) = 0 Reorder the terms: (-3 + 4x2) + -1(x2 + x + 1) = 0 Remove parenthesis around (-3 + 4x2) -3 + 4x2 + -1(x2 + x + 1) = 0 Reorder the terms: -3 + 4x2 + -1(1 + x + x2) = 0 -3 + 4x2 + (1 * -1 + x * -1 + x2 * -1) = 0 -3 + 4x2 + (-1 + -1x + -1x2) = 0 Reorder the terms: -3 + -1 + -1x + 4x2 + -1x2 = 0 Combine like terms: -3 + -1 = -4 -4 + -1x + 4x2 + -1x2 = 0 Combine like terms: 4x2 + -1x2 = 3x2 -4 + -1x + 3x2 = 0 Solving -4 + -1x + 3x2 = 0 Solving for variable 'x'. Factor a trinomial. (-1 + -1x)(4 + -3x) = 0Subproblem 1
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 = -1Subproblem 2
Set the factor '(4 + -3x)' equal to zero and attempt to solve: Simplifying 4 + -3x = 0 Solving 4 + -3x = 0 Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -3x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -3x = 0 + -4 -3x = 0 + -4 Combine like terms: 0 + -4 = -4 -3x = -4 Divide each side by '-3'. x = 1.333333333 Simplifying x = 1.333333333Solution
x = {-1, 1.333333333}
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