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Simplifying 7x2 + -5x = x2 + 4 Reorder the terms: -5x + 7x2 = x2 + 4 Reorder the terms: -5x + 7x2 = 4 + x2 Solving -5x + 7x2 = 4 + x2 Solving for variable 'x'. Reorder the terms: -4 + -5x + 7x2 + -1x2 = 4 + x2 + -4 + -1x2 Combine like terms: 7x2 + -1x2 = 6x2 -4 + -5x + 6x2 = 4 + x2 + -4 + -1x2 Reorder the terms: -4 + -5x + 6x2 = 4 + -4 + x2 + -1x2 Combine like terms: 4 + -4 = 0 -4 + -5x + 6x2 = 0 + x2 + -1x2 -4 + -5x + 6x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -4 + -5x + 6x2 = 0 Factor a trinomial. (-1 + -2x)(4 + -3x) = 0Subproblem 1
Set the factor '(-1 + -2x)' equal to zero and attempt to solve: Simplifying -1 + -2x = 0 Solving -1 + -2x = 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 + -2x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -2x = 0 + 1 -2x = 0 + 1 Combine like terms: 0 + 1 = 1 -2x = 1 Divide each side by '-2'. x = -0.5 Simplifying x = -0.5Subproblem 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 = {-0.5, 1.333333333}
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