Solve 1-a^2-10a+25

$$1 - a ^ { 2 } - 10 a + 25$$

Factor

$$-\left(a-\left(-\sqrt{51}-5\right)\right)\left(a-\left(\sqrt{51}-5\right)\right)$$

Steps Using the Quadratic Formula

Add 1 and 25 to get 26.

$$factor(26-a^{2}-10a)$$

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.

$$-a^{2}-10a+26=0$$

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.

$$a=\frac{-\left(-10\right)±\sqrt{\left(-10\right)^{2}-4\left(-1\right)\times 26}}{2\left(-1\right)}$$

Square -10.

$$a=\frac{-\left(-10\right)±\sqrt{100-4\left(-1\right)\times 26}}{2\left(-1\right)}$$

Multiply -4 times -1.

$$a=\frac{-\left(-10\right)±\sqrt{100+4\times 26}}{2\left(-1\right)}$$

Multiply 4 times 26.

$$a=\frac{-\left(-10\right)±\sqrt{100+104}}{2\left(-1\right)}$$

Add 100 to 104.

$$a=\frac{-\left(-10\right)±\sqrt{204}}{2\left(-1\right)}$$

Take the square root of 204.

$$a=\frac{-\left(-10\right)±2\sqrt{51}}{2\left(-1\right)}$$

The opposite of -10 is 10.

$$a=\frac{10±2\sqrt{51}}{2\left(-1\right)}$$

Multiply 2 times -1.

$$a=\frac{10±2\sqrt{51}}{-2}$$

Now solve the equation a=\frac{10±2\sqrt{51}}{-2} when ± is plus. Add 10 to 2\sqrt{51}.

$$a=\frac{2\sqrt{51}+10}{-2}$$

Divide 10+2\sqrt{51} by -2.

$$a=-\left(\sqrt{51}+5\right)$$

Now solve the equation a=\frac{10±2\sqrt{51}}{-2} when ± is minus. Subtract 2\sqrt{51} from 10.

$$a=\frac{10-2\sqrt{51}}{-2}$$

Divide 10-2\sqrt{51} by -2.

$$a=\sqrt{51}-5$$

Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute -\left(5+\sqrt{51}\right) for x_{1} and -5+\sqrt{51} for x_{2}.

$$-a^{2}-10a+26=-\left(a-\left(-\left(\sqrt{51}+5\right)\right)\right)\left(a-\left(\sqrt{51}-5\right)\right)$$

Evaluate

$$26-10a-a^{2}$$

Solution Steps

Add 1 and 25 to get 26.

$$26-a^{2}-10a$$