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Simplifying 5x + 3x = x2 + 7 Combine like terms: 5x + 3x = 8x 8x = x2 + 7 Reorder the terms: 8x = 7 + x2 Solving 8x = 7 + x2 Solving for variable 'x'. Reorder the terms: -7 + 8x + -1x2 = 7 + x2 + -7 + -1x2 Reorder the terms: -7 + 8x + -1x2 = 7 + -7 + x2 + -1x2 Combine like terms: 7 + -7 = 0 -7 + 8x + -1x2 = 0 + x2 + -1x2 -7 + 8x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -7 + 8x + -1x2 = 0 Factor a trinomial. (-7 + x)(1 + -1x) = 0Subproblem 1
Set the factor '(-7 + x)' equal to zero and attempt to solve: Simplifying -7 + x = 0 Solving -7 + x = 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 + x = 0 + 7 Combine like terms: -7 + 7 = 0 0 + x = 0 + 7 x = 0 + 7 Combine like terms: 0 + 7 = 7 x = 7 Simplifying x = 7Subproblem 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 = {7, 1}
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