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Simplifying 5x2 + -3x = x2 + 7 Reorder the terms: -3x + 5x2 = x2 + 7 Reorder the terms: -3x + 5x2 = 7 + x2 Solving -3x + 5x2 = 7 + x2 Solving for variable 'x'. Reorder the terms: -7 + -3x + 5x2 + -1x2 = 7 + x2 + -7 + -1x2 Combine like terms: 5x2 + -1x2 = 4x2 -7 + -3x + 4x2 = 7 + x2 + -7 + -1x2 Reorder the terms: -7 + -3x + 4x2 = 7 + -7 + x2 + -1x2 Combine like terms: 7 + -7 = 0 -7 + -3x + 4x2 = 0 + x2 + -1x2 -7 + -3x + 4x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -7 + -3x + 4x2 = 0 Factor a trinomial. (-1 + -1x)(7 + -4x) = 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 '(7 + -4x)' equal to zero and attempt to solve: Simplifying 7 + -4x = 0 Solving 7 + -4x = 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 + -4x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -4x = 0 + -7 -4x = 0 + -7 Combine like terms: 0 + -7 = -7 -4x = -7 Divide each side by '-4'. x = 1.75 Simplifying x = 1.75Solution
x = {-1, 1.75}
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