Solve 4-x*x-4*x-4*x+10

$$4 - x \cdot x - 4 \cdot x - 4 \cdot x + 10$$

Evaluate

$$14-8x-x^{2}$$

Solution Steps

Multiply x and x to get x^{2}.

$$4-x^{2}-4x-4x+10$$

Combine -4x and -4x to get -8x.

$$4-x^{2}-8x+10$$

Add 4 and 10 to get 14.

$$14-x^{2}-8x$$

Factor

$$-\left(x-\left(-\sqrt{30}-4\right)\right)\left(x-\left(\sqrt{30}-4\right)\right)$$

Steps Using the Quadratic Formula

Multiply x and x to get x^{2}.

$$factor(4-x^{2}-4x-4x+10)$$

Combine -4x and -4x to get -8x.

$$factor(4-x^{2}-8x+10)$$

Add 4 and 10 to get 14.

$$factor(14-x^{2}-8x)$$

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.

$$-x^{2}-8x+14=0$$

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.

$$x=\frac{-\left(-8\right)±\sqrt{\left(-8\right)^{2}-4\left(-1\right)\times 14}}{2\left(-1\right)}$$

Square -8.

$$x=\frac{-\left(-8\right)±\sqrt{64-4\left(-1\right)\times 14}}{2\left(-1\right)}$$

Multiply -4 times -1.

$$x=\frac{-\left(-8\right)±\sqrt{64+4\times 14}}{2\left(-1\right)}$$

Multiply 4 times 14.

$$x=\frac{-\left(-8\right)±\sqrt{64+56}}{2\left(-1\right)}$$

Add 64 to 56.

$$x=\frac{-\left(-8\right)±\sqrt{120}}{2\left(-1\right)}$$

Take the square root of 120.

$$x=\frac{-\left(-8\right)±2\sqrt{30}}{2\left(-1\right)}$$

The opposite of -8 is 8.

$$x=\frac{8±2\sqrt{30}}{2\left(-1\right)}$$

Multiply 2 times -1.

$$x=\frac{8±2\sqrt{30}}{-2}$$

Now solve the equation x=\frac{8±2\sqrt{30}}{-2} when ± is plus. Add 8 to 2\sqrt{30}.

$$x=\frac{2\sqrt{30}+8}{-2}$$

Divide 8+2\sqrt{30} by -2.

$$x=-\left(\sqrt{30}+4\right)$$

Now solve the equation x=\frac{8±2\sqrt{30}}{-2} when ± is minus. Subtract 2\sqrt{30} from 8.

$$x=\frac{8-2\sqrt{30}}{-2}$$

Divide 8-2\sqrt{30} by -2.

$$x=\sqrt{30}-4$$

Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute -\left(4+\sqrt{30}\right) for x_{1} and -4+\sqrt{30} for x_{2}.

$$-x^{2}-8x+14=-\left(x-\left(-\left(\sqrt{30}+4\right)\right)\right)\left(x-\left(\sqrt{30}-4\right)\right)$$