Solve 9x^2-24x+21

$$9 { x }^{ 2 } -24x+21$$

Factor

$$3\left(3x^{2}-8x+7\right)$$

Solution Steps

Factor out 3. Polynomial 3x^{2}-8x+7 is not factored since it does not have any rational roots.

$$3\left(3x^{2}-8x+7\right)$$

Steps Using the Quadratic Formula

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.

$$9x^{2}-24x+21=0$$

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.

$$x=\frac{-\left(-24\right)±\sqrt{\left(-24\right)^{2}-4\times 9\times 21}}{2\times 9}$$

Square -24.

$$x=\frac{-\left(-24\right)±\sqrt{576-4\times 9\times 21}}{2\times 9}$$

Multiply -4 times 9.

$$x=\frac{-\left(-24\right)±\sqrt{576-36\times 21}}{2\times 9}$$

Multiply -36 times 21.

$$x=\frac{-\left(-24\right)±\sqrt{576-756}}{2\times 9}$$

Add 576 to -756.

$$x=\frac{-\left(-24\right)±\sqrt{-180}}{2\times 9}$$

Since the square root of a negative number is not defined in the real field, there are no solutions. Quadratic polynomial cannot be factored.

$$9x^{2}-24x+21$$

Evaluate

$$9x^{2}-24x+21$$