Solve (148x^2-582x+58356)

$$( 148 x ^ { 2 } - 582 x + 58356 )$$

Factor

$$2\left(74x^{2}-291x+29178\right)$$

Solution Steps

Factor out 2. Polynomial 74x^{2}-291x+29178 is not factored since it does not have any rational roots.

$$2\left(74x^{2}-291x+29178\right)$$

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.

$$148x^{2}-582x+58356=0$$

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.

$$x=\frac{-\left(-582\right)±\sqrt{\left(-582\right)^{2}-4\times 148\times 58356}}{2\times 148}$$

Square -582.

$$x=\frac{-\left(-582\right)±\sqrt{338724-4\times 148\times 58356}}{2\times 148}$$

Multiply -4 times 148.

$$x=\frac{-\left(-582\right)±\sqrt{338724-592\times 58356}}{2\times 148}$$

Multiply -592 times 58356.

$$x=\frac{-\left(-582\right)±\sqrt{338724-34546752}}{2\times 148}$$

Add 338724 to -34546752.

$$x=\frac{-\left(-582\right)±\sqrt{-34208028}}{2\times 148}$$

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

$$148x^{2}-582x+58356$$

Evaluate

$$148x^{2}-582x+58356$$