Solve x^2-100+0x

$$x ^ { 2 } - 100 + 0 x$$

Evaluate

$$x^{2}-100$$

Solution Steps

Anything times zero gives zero.

$$x^{2}-100+0$$

Add -100 and 0 to get -100.

$$x^{2}-100$$

Factor

$$\left(x-10\right)\left(x+10\right)$$

Solution Steps

Multiply and combine like terms.

$$x^{2}-100$$

Rewrite x^{2}-100 as x^{2}-10^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(x-10\right)\left(x+10\right)$$

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.

$$x^{2}-100=0$$

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.

$$x=\frac{0±\sqrt{0^{2}-4\left(-100\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-100\right)}}{2}$$

Multiply -4 times -100.

$$x=\frac{0±\sqrt{400}}{2}$$

Take the square root of 400.

$$x=\frac{0±20}{2}$$

Now solve the equation x=\frac{±20}{2} when ± is plus. Divide 20 by 2.

$$x=10$$

Now solve the equation x=\frac{±20}{2} when ± is minus. Divide -20 by 2.

$$x=-10$$

Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute 10 for x_{1} and -10 for x_{2}.

$$x^{2}-100=\left(x-10\right)\left(x-\left(-10\right)\right)$$

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

$$x^{2}-100=\left(x-10\right)\left(x+10\right)$$