Solve 72x^2-98=0?

$$72 x ^ { 2 } - 98 = 0 ?$$

Solve for x

$$x = \frac{7}{6} = 1\frac{1}{6} \approx 1.166666667$$

$$x = -\frac{7}{6} = -1\frac{1}{6} \approx -1.166666667$$

Steps Using Difference of Squares

Divide both sides by 2.

$$36x^{2}-49=0$$

Consider 36x^{2}-49. Rewrite 36x^{2}-49 as \left(6x\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).

$$\left(6x-7\right)\left(6x+7\right)=0$$

To find equation solutions, solve 6x-7=0 and 6x+7=0.

$$x=\frac{7}{6} x=-\frac{7}{6}$$

Steps by Finding Square Root

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

$$72x^{2}=98$$

Divide both sides by 72.

$$x^{2}=\frac{98}{72}$$

Reduce the fraction \frac{98}{72} to lowest terms by extracting and canceling out 2.

$$x^{2}=\frac{49}{36}$$

Take the square root of both sides of the equation.

$$x=\frac{7}{6} x=-\frac{7}{6}$$

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.

$$72x^{2}-98=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 72 for a, 0 for b, and -98 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 72\left(-98\right)}}{2\times 72}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 72\left(-98\right)}}{2\times 72}$$

Multiply -4 times 72.

$$x=\frac{0±\sqrt{-288\left(-98\right)}}{2\times 72}$$

Multiply -288 times -98.

$$x=\frac{0±\sqrt{28224}}{2\times 72}$$

Take the square root of 28224.

$$x=\frac{0±168}{2\times 72}$$

Multiply 2 times 72.

$$x=\frac{0±168}{144}$$

Now solve the equation x=\frac{0±168}{144} when ± is plus. Reduce the fraction \frac{168}{144} to lowest terms by extracting and canceling out 24.

$$x=\frac{7}{6}$$

Now solve the equation x=\frac{0±168}{144} when ± is minus. Reduce the fraction \frac{-168}{144} to lowest terms by extracting and canceling out 24.

$$x=-\frac{7}{6}$$

The equation is now solved.

$$x=\frac{7}{6} x=-\frac{7}{6}$$