Solve -4x^2-64x-262

$$-4 { x }^{ 2 } -64x-262$$

Factor

$$2\left(-2x^{2}-32x-131\right)$$

Solution Steps

Factor out 2. Polynomial -2x^{2}-32x-131 is not factored since it does not have any rational roots.

$$2\left(-2x^{2}-32x-131\right)$$

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.

$$-4x^{2}-64x-262=0$$

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.

$$x=\frac{-\left(-64\right)±\sqrt{\left(-64\right)^{2}-4\left(-4\right)\left(-262\right)}}{2\left(-4\right)}$$

Square -64.

$$x=\frac{-\left(-64\right)±\sqrt{4096-4\left(-4\right)\left(-262\right)}}{2\left(-4\right)}$$

Multiply -4 times -4.

$$x=\frac{-\left(-64\right)±\sqrt{4096+16\left(-262\right)}}{2\left(-4\right)}$$

Multiply 16 times -262.

$$x=\frac{-\left(-64\right)±\sqrt{4096-4192}}{2\left(-4\right)}$$

Add 4096 to -4192.

$$x=\frac{-\left(-64\right)±\sqrt{-96}}{2\left(-4\right)}$$

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

$$-4x^{2}-64x-262$$

Evaluate

$$-4x^{2}-64x-262$$