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Simplifying x(7x + 26) = 2x2 + -7x + 14 Reorder the terms: x(26 + 7x) = 2x2 + -7x + 14 (26 * x + 7x * x) = 2x2 + -7x + 14 (26x + 7x2) = 2x2 + -7x + 14 Reorder the terms: 26x + 7x2 = 14 + -7x + 2x2 Solving 26x + 7x2 = 14 + -7x + 2x2 Solving for variable 'x'. Reorder the terms: -14 + 26x + 7x + 7x2 + -2x2 = 14 + -7x + 2x2 + -14 + 7x + -2x2 Combine like terms: 26x + 7x = 33x -14 + 33x + 7x2 + -2x2 = 14 + -7x + 2x2 + -14 + 7x + -2x2 Combine like terms: 7x2 + -2x2 = 5x2 -14 + 33x + 5x2 = 14 + -7x + 2x2 + -14 + 7x + -2x2 Reorder the terms: -14 + 33x + 5x2 = 14 + -14 + -7x + 7x + 2x2 + -2x2 Combine like terms: 14 + -14 = 0 -14 + 33x + 5x2 = 0 + -7x + 7x + 2x2 + -2x2 -14 + 33x + 5x2 = -7x + 7x + 2x2 + -2x2 Combine like terms: -7x + 7x = 0 -14 + 33x + 5x2 = 0 + 2x2 + -2x2 -14 + 33x + 5x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 -14 + 33x + 5x2 = 0 Factor a trinomial. (-7 + -1x)(2 + -5x) = 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 '(2 + -5x)' equal to zero and attempt to solve: Simplifying 2 + -5x = 0 Solving 2 + -5x = 0 Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -5x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -5x = 0 + -2 -5x = 0 + -2 Combine like terms: 0 + -2 = -2 -5x = -2 Divide each side by '-5'. x = 0.4 Simplifying x = 0.4Solution
x = {-7, 0.4}
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