Solve 5x^2+15-5x

$$5 x ^ { 2 } + 15 - 5 x$$

Factor

$$5\left(x^{2}-x+3\right)$$

Solution Steps

Factor out 5. Polynomial x^{2}+3-x is not factored since it does not have any rational roots.

$$5\left(x^{2}+3-x\right)$$

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.

$$5x^{2}-5x+15=0$$

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.

$$x=\frac{-\left(-5\right)±\sqrt{\left(-5\right)^{2}-4\times 5\times 15}}{2\times 5}$$

Square -5.

$$x=\frac{-\left(-5\right)±\sqrt{25-4\times 5\times 15}}{2\times 5}$$

Multiply -4 times 5.

$$x=\frac{-\left(-5\right)±\sqrt{25-20\times 15}}{2\times 5}$$

Multiply -20 times 15.

$$x=\frac{-\left(-5\right)±\sqrt{25-300}}{2\times 5}$$

Add 25 to -300.

$$x=\frac{-\left(-5\right)±\sqrt{-275}}{2\times 5}$$

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

$$5x^{2}-5x+15$$

Evaluate

$$5\left(x^{2}-x+3\right)$$