Solve 9x^2-100=0

$$9 x ^ { 2 } - 100 = 0$$

Solve for x

$$x = \frac{10}{3} = 3\frac{1}{3} \approx 3.333333333$$

$$x = -\frac{10}{3} = -3\frac{1}{3} \approx -3.333333333$$

Steps Using Difference of Squares

Consider 9x^{2}-100. Rewrite 9x^{2}-100 as \left(3x\right)^{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).

$$\left(3x-10\right)\left(3x+10\right)=0$$

To find equation solutions, solve 3x-10=0 and 3x+10=0.

$$x=\frac{10}{3} x=-\frac{10}{3}$$

Steps by Finding Square Root

Add 100 to both sides. Anything plus zero gives itself.

$$9x^{2}=100$$

Divide both sides by 9.

$$x^{2}=\frac{100}{9}$$

Take the square root of both sides of the equation.

$$x=\frac{10}{3} x=-\frac{10}{3}$$

Steps Using the Quadratic Formula

Quadratic equations like this one, with an x^{2} term but no x term, can still be solved using the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}, once they are put in standard form: ax^{2}+bx+c=0.

$$9x^{2}-100=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 9 for a, 0 for b, and -100 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 9\left(-100\right)}}{2\times 9}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 9\left(-100\right)}}{2\times 9}$$

Multiply -4 times 9.

$$x=\frac{0±\sqrt{-36\left(-100\right)}}{2\times 9}$$

Multiply -36 times -100.

$$x=\frac{0±\sqrt{3600}}{2\times 9}$$

Take the square root of 3600.

$$x=\frac{0±60}{2\times 9}$$

Multiply 2 times 9.

$$x=\frac{0±60}{18}$$

Now solve the equation x=\frac{0±60}{18} when ± is plus. Reduce the fraction \frac{60}{18} to lowest terms by extracting and canceling out 6.

$$x=\frac{10}{3}$$

Now solve the equation x=\frac{0±60}{18} when ± is minus. Reduce the fraction \frac{-60}{18} to lowest terms by extracting and canceling out 6.

$$x=-\frac{10}{3}$$

The equation is now solved.

$$x=\frac{10}{3} x=-\frac{10}{3}$$