Solve x^2+0x-1

$${ x }^{ 2 } +0x-1$$

Evaluate

$$x^{2}-1$$

Solution Steps

Anything times zero gives zero.

$$x^{2}+0-1$$

Subtract 1 from 0 to get -1.

$$x^{2}-1$$

Factor

$$\left(x-1\right)\left(x+1\right)$$

Solution Steps

Multiply and combine like terms.

$$x^{2}-1$$

Rewrite x^{2}-1 as x^{2}-1^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(x-1\right)\left(x+1\right)$$

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.

$$x^{2}-1=0$$

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.

$$x=\frac{0±\sqrt{0^{2}-4\left(-1\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-1\right)}}{2}$$

Multiply -4 times -1.

$$x=\frac{0±\sqrt{4}}{2}$$

Take the square root of 4.

$$x=\frac{0±2}{2}$$

Now solve the equation x=\frac{±2}{2} when ± is plus. Divide 2 by 2.

$$x=1$$

Now solve the equation x=\frac{±2}{2} when ± is minus. Divide -2 by 2.

$$x=-1$$

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

$$x^{2}-1=\left(x-1\right)\left(x-\left(-1\right)\right)$$

Simplify all the expressions of the form p-\left(-q\right) to p+q.

$$x^{2}-1=\left(x-1\right)\left(x+1\right)$$