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Simplifying x(2x + 13) = 7 Reorder the terms: x(13 + 2x) = 7 (13 * x + 2x * x) = 7 (13x + 2x2) = 7 Solving 13x + 2x2 = 7 Solving for variable 'x'. Reorder the terms: -7 + 13x + 2x2 = 7 + -7 Combine like terms: 7 + -7 = 0 -7 + 13x + 2x2 = 0 Factor a trinomial. (-7 + -1x)(1 + -2x) = 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 '(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 = {-7, 0.5}
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