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Simplifying 9x(x + -5) = (2x + 1)(9x + -5) Reorder the terms: 9x(-5 + x) = (2x + 1)(9x + -5) (-5 * 9x + x * 9x) = (2x + 1)(9x + -5) (-45x + 9x2) = (2x + 1)(9x + -5) Reorder the terms: -45x + 9x2 = (1 + 2x)(9x + -5) Reorder the terms: -45x + 9x2 = (1 + 2x)(-5 + 9x) Multiply (1 + 2x) * (-5 + 9x) -45x + 9x2 = (1(-5 + 9x) + 2x * (-5 + 9x)) -45x + 9x2 = ((-5 * 1 + 9x * 1) + 2x * (-5 + 9x)) -45x + 9x2 = ((-5 + 9x) + 2x * (-5 + 9x)) -45x + 9x2 = (-5 + 9x + (-5 * 2x + 9x * 2x)) -45x + 9x2 = (-5 + 9x + (-10x + 18x2)) Combine like terms: 9x + -10x = -1x -45x + 9x2 = (-5 + -1x + 18x2) Solving -45x + 9x2 = -5 + -1x + 18x2 Solving for variable 'x'. Reorder the terms: 5 + -45x + x + 9x2 + -18x2 = -5 + -1x + 18x2 + 5 + x + -18x2 Combine like terms: -45x + x = -44x 5 + -44x + 9x2 + -18x2 = -5 + -1x + 18x2 + 5 + x + -18x2 Combine like terms: 9x2 + -18x2 = -9x2 5 + -44x + -9x2 = -5 + -1x + 18x2 + 5 + x + -18x2 Reorder the terms: 5 + -44x + -9x2 = -5 + 5 + -1x + x + 18x2 + -18x2 Combine like terms: -5 + 5 = 0 5 + -44x + -9x2 = 0 + -1x + x + 18x2 + -18x2 5 + -44x + -9x2 = -1x + x + 18x2 + -18x2 Combine like terms: -1x + x = 0 5 + -44x + -9x2 = 0 + 18x2 + -18x2 5 + -44x + -9x2 = 18x2 + -18x2 Combine like terms: 18x2 + -18x2 = 0 5 + -44x + -9x2 = 0 Factor a trinomial. (1 + -9x)(5 + x) = 0Subproblem 1
Set the factor '(1 + -9x)' equal to zero and attempt to solve: Simplifying 1 + -9x = 0 Solving 1 + -9x = 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 + -9x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -9x = 0 + -1 -9x = 0 + -1 Combine like terms: 0 + -1 = -1 -9x = -1 Divide each side by '-9'. x = 0.1111111111 Simplifying x = 0.1111111111Subproblem 2
Set the factor '(5 + x)' equal to zero and attempt to solve: Simplifying 5 + x = 0 Solving 5 + x = 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 + x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + x = 0 + -5 x = 0 + -5 Combine like terms: 0 + -5 = -5 x = -5 Simplifying x = -5Solution
x = {0.1111111111, -5}
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