Solve 18x^2=49/2

$$18 x ^ { 2 } = \frac { 49 } { 2 }$$

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 18.

$$x^{2}=\frac{\frac{49}{2}}{18}$$

Express \frac{\frac{49}{2}}{18} as a single fraction.

$$x^{2}=\frac{49}{2\times 18}$$

Multiply 2 and 18 to get 36.

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

Subtract \frac{49}{36} from both sides.

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

Multiply both sides by 36.

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

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

Divide both sides by 18.

$$x^{2}=\frac{\frac{49}{2}}{18}$$

Express \frac{\frac{49}{2}}{18} as a single fraction.

$$x^{2}=\frac{49}{2\times 18}$$

Multiply 2 and 18 to get 36.

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

Take the square root of both sides of the equation.

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

Steps Using the Quadratic Formula

Divide both sides by 18.

$$x^{2}=\frac{\frac{49}{2}}{18}$$

Express \frac{\frac{49}{2}}{18} as a single fraction.

$$x^{2}=\frac{49}{2\times 18}$$

Multiply 2 and 18 to get 36.

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

Subtract \frac{49}{36} from both sides.

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

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -\frac{49}{36} for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-\frac{49}{36}\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-\frac{49}{36}\right)}}{2}$$

Multiply -4 times -\frac{49}{36}.

$$x=\frac{0±\sqrt{\frac{49}{9}}}{2}$$

Take the square root of \frac{49}{9}.

$$x=\frac{0±\frac{7}{3}}{2}$$

Now solve the equation x=\frac{0±\frac{7}{3}}{2} when ± is plus.

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

Now solve the equation x=\frac{0±\frac{7}{3}}{2} when ± is minus.

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

The equation is now solved.

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