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Simplifying x2 + 5x = 21 + x Reorder the terms: 5x + x2 = 21 + x Solving 5x + x2 = 21 + x Solving for variable 'x'. Reorder the terms: -21 + 5x + -1x + x2 = 21 + x + -21 + -1x Combine like terms: 5x + -1x = 4x -21 + 4x + x2 = 21 + x + -21 + -1x Reorder the terms: -21 + 4x + x2 = 21 + -21 + x + -1x Combine like terms: 21 + -21 = 0 -21 + 4x + x2 = 0 + x + -1x -21 + 4x + x2 = x + -1x Combine like terms: x + -1x = 0 -21 + 4x + x2 = 0 Factor a trinomial. (-7 + -1x)(3 + -1x) = 0Subproblem 1
Set the factor '(-7 + -1x)' equal to zero and attempt to solve: Simplifying -7 + -1x = 0 Solving -7 + -1x = 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 + -1x = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -1x = 0 + 7 -1x = 0 + 7 Combine like terms: 0 + 7 = 7 -1x = 7 Divide each side by '-1'. x = -7 Simplifying x = -7Subproblem 2
Set the factor '(3 + -1x)' equal to zero and attempt to solve: Simplifying 3 + -1x = 0 Solving 3 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -1x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1x = 0 + -3 -1x = 0 + -3 Combine like terms: 0 + -3 = -3 -1x = -3 Divide each side by '-1'. x = 3 Simplifying x = 3Solution
x = {-7, 3}
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