Solve 18x^2-98=0

$$18 x ^ { 2 } - 98 = 0$$

Solve for x

$$x = \frac{7}{3} = 2\frac{1}{3} \approx 2.333333333$$

$$x = -\frac{7}{3} = -2\frac{1}{3} \approx -2.333333333$$

Steps Using Difference of Squares

Divide both sides by 2.

$$9x^{2}-49=0$$

Consider 9x^{2}-49. Rewrite 9x^{2}-49 as \left(3x\right)^{2}-7^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(3x-7\right)\left(3x+7\right)=0$$

To find equation solutions, solve 3x-7=0 and 3x+7=0.

$$x=\frac{7}{3} x=-\frac{7}{3}$$

Steps by Finding Square Root

Add 98 to both sides. Anything plus zero gives itself.

$$18x^{2}=98$$

Divide both sides by 18.

$$x^{2}=\frac{98}{18}$$

Reduce the fraction \frac{98}{18} to lowest terms by extracting and canceling out 2.

$$x^{2}=\frac{49}{9}$$

Take the square root of both sides of the equation.

$$x=\frac{7}{3} x=-\frac{7}{3}$$

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.

$$18x^{2}-98=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 18 for a, 0 for b, and -98 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 18\left(-98\right)}}{2\times 18}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 18\left(-98\right)}}{2\times 18}$$

Multiply -4 times 18.

$$x=\frac{0±\sqrt{-72\left(-98\right)}}{2\times 18}$$

Multiply -72 times -98.

$$x=\frac{0±\sqrt{7056}}{2\times 18}$$

Take the square root of 7056.

$$x=\frac{0±84}{2\times 18}$$

Multiply 2 times 18.

$$x=\frac{0±84}{36}$$

Now solve the equation x=\frac{0±84}{36} when ± is plus. Reduce the fraction \frac{84}{36} to lowest terms by extracting and canceling out 12.

$$x=\frac{7}{3}$$

Now solve the equation x=\frac{0±84}{36} when ± is minus. Reduce the fraction \frac{-84}{36} to lowest terms by extracting and canceling out 12.

$$x=-\frac{7}{3}$$

The equation is now solved.

$$x=\frac{7}{3} x=-\frac{7}{3}$$