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Simplifying 4x2 = 7 + -12x Solving 4x2 = 7 + -12x Solving for variable 'x'. Reorder the terms: -7 + 12x + 4x2 = 7 + -12x + -7 + 12x Reorder the terms: -7 + 12x + 4x2 = 7 + -7 + -12x + 12x Combine like terms: 7 + -7 = 0 -7 + 12x + 4x2 = 0 + -12x + 12x -7 + 12x + 4x2 = -12x + 12x Combine like terms: -12x + 12x = 0 -7 + 12x + 4x2 = 0 Factor a trinomial. (-7 + -2x)(1 + -2x) = 0Subproblem 1
Set the factor '(-7 + -2x)' equal to zero and attempt to solve: Simplifying -7 + -2x = 0 Solving -7 + -2x = 0 Move all terms containing x to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + -2x = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -2x = 0 + 7 -2x = 0 + 7 Combine like terms: 0 + 7 = 7 -2x = 7 Divide each side by '-2'. x = -3.5 Simplifying x = -3.5Subproblem 2
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 = 0.5Solution
x = {-3.5, 0.5}
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