Solve x^2*3^5=4

$$x ^ { 2 } \times 3 ^ { 5 } = 4$$

Solve for x

$$x=\frac{2\sqrt{3}}{27}\approx 0.12830006$$

$$x=-\frac{2\sqrt{3}}{27}\approx -0.12830006$$

Steps by Finding Square Root

Calculate 3 to the power of 5 and get 243.

$$x^{2}\times 243=4$$

Divide both sides by 243.

$$x^{2}=\frac{4}{243}$$

Take the square root of both sides of the equation.

$$x=\frac{2\sqrt{3}}{27} x=-\frac{2\sqrt{3}}{27}$$

Steps Using the Quadratic Formula

Calculate 3 to the power of 5 and get 243.

$$x^{2}\times 243=4$$

Subtract 4 from both sides.

$$x^{2}\times 243-4=0$$

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.

$$243x^{2}-4=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 243 for a, 0 for b, and -4 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 243\left(-4\right)}}{2\times 243}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 243\left(-4\right)}}{2\times 243}$$

Multiply -4 times 243.

$$x=\frac{0±\sqrt{-972\left(-4\right)}}{2\times 243}$$

Multiply -972 times -4.

$$x=\frac{0±\sqrt{3888}}{2\times 243}$$

Take the square root of 3888.

$$x=\frac{0±36\sqrt{3}}{2\times 243}$$

Multiply 2 times 243.

$$x=\frac{0±36\sqrt{3}}{486}$$

Now solve the equation x=\frac{0±36\sqrt{3}}{486} when ± is plus.

$$x=\frac{2\sqrt{3}}{27}$$

Now solve the equation x=\frac{0±36\sqrt{3}}{486} when ± is minus.

$$x=-\frac{2\sqrt{3}}{27}$$

The equation is now solved.

$$x=\frac{2\sqrt{3}}{27} x=-\frac{2\sqrt{3}}{27}$$