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Simplifying x(2x + 3) = 77 Reorder the terms: x(3 + 2x) = 77 (3 * x + 2x * x) = 77 (3x + 2x2) = 77 Solving 3x + 2x2 = 77 Solving for variable 'x'. Reorder the terms: -77 + 3x + 2x2 = 77 + -77 Combine like terms: 77 + -77 = 0 -77 + 3x + 2x2 = 0 Factor a trinomial. (-7 + -1x)(11 + -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 '(11 + -2x)' equal to zero and attempt to solve: Simplifying 11 + -2x = 0 Solving 11 + -2x = 0 Move all terms containing x to the left, all other terms to the right. Add '-11' to each side of the equation. 11 + -11 + -2x = 0 + -11 Combine like terms: 11 + -11 = 0 0 + -2x = 0 + -11 -2x = 0 + -11 Combine like terms: 0 + -11 = -11 -2x = -11 Divide each side by '-2'. x = 5.5 Simplifying x = 5.5Solution
x = {-7, 5.5}
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