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x\left(9x-5\right)
Factor out x.
9x^{2}-5x=0
Quadratic polynomial can be factored using the transformation ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right), where x_{1} and x_{2} are the solutions of the quadratic equation ax^{2}+bx+c=0.
x=\frac{-\left(-5\right)±\sqrt{\left(-5\right)^{2}}}{2\times 9}
All equations of the form ax^{2}+bx+c=0 can be solved using the quadratic formula: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. The quadratic formula gives two solutions, one when ± is addition and one when it is subtraction.
x=\frac{-\left(-5\right)±5}{2\times 9}
Take the square root of \left(-5\right)^{2}.
x=\frac{5±5}{2\times 9}
The opposite of -5 is 5.
x=\frac{5±5}{18}
Multiply 2 times 9.
x=\frac{10}{18}
Now solve the equation x=\frac{5±5}{18} when ± is plus. Add 5 to 5.
x=\frac{5}{9}
Reduce the fraction \frac{10}{18} to lowest terms by extracting and canceling out 2.
x=\frac{0}{18}
Now solve the equation x=\frac{5±5}{18} when ± is minus. Subtract 5 from 5.
x=0
Divide 0 by 18.
9x^{2}-5x=9\left(x-\frac{5}{9}\right)x
Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute \frac{5}{9} for x_{1} and 0 for x_{2}.
9x^{2}-5x=9\times \frac{9x-5}{9}x
Subtract \frac{5}{9} from x by finding a common denominator and subtracting the numerators. Then reduce the fraction to lowest terms if possible.
9x^{2}-5x=\left(9x-5\right)x
Cancel out 9, the greatest common factor in 9 and 9.