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Simplifying x(7x + 19) = 2x2 + -4x + 10 Reorder the terms: x(19 + 7x) = 2x2 + -4x + 10 (19 * x + 7x * x) = 2x2 + -4x + 10 (19x + 7x2) = 2x2 + -4x + 10 Reorder the terms: 19x + 7x2 = 10 + -4x + 2x2 Solving 19x + 7x2 = 10 + -4x + 2x2 Solving for variable 'x'. Reorder the terms: -10 + 19x + 4x + 7x2 + -2x2 = 10 + -4x + 2x2 + -10 + 4x + -2x2 Combine like terms: 19x + 4x = 23x -10 + 23x + 7x2 + -2x2 = 10 + -4x + 2x2 + -10 + 4x + -2x2 Combine like terms: 7x2 + -2x2 = 5x2 -10 + 23x + 5x2 = 10 + -4x + 2x2 + -10 + 4x + -2x2 Reorder the terms: -10 + 23x + 5x2 = 10 + -10 + -4x + 4x + 2x2 + -2x2 Combine like terms: 10 + -10 = 0 -10 + 23x + 5x2 = 0 + -4x + 4x + 2x2 + -2x2 -10 + 23x + 5x2 = -4x + 4x + 2x2 + -2x2 Combine like terms: -4x + 4x = 0 -10 + 23x + 5x2 = 0 + 2x2 + -2x2 -10 + 23x + 5x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 -10 + 23x + 5x2 = 0 Factor a trinomial. (-5 + -1x)(2 + -5x) = 0Subproblem 1
Set the factor '(-5 + -1x)' equal to zero and attempt to solve: Simplifying -5 + -1x = 0 Solving -5 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + -1x = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -1x = 0 + 5 -1x = 0 + 5 Combine like terms: 0 + 5 = 5 -1x = 5 Divide each side by '-1'. x = -5 Simplifying x = -5Subproblem 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 = {-5, 0.4}
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