Solve 34.8=x(3(x))

$$34.8 = x ( 3 ( x ) )$$

Solve for x

$$x = \frac{\sqrt{290}}{5} \approx 3.405877273$$

$$x = -\frac{\sqrt{290}}{5} \approx -3.405877273$$

Steps by Finding Square Root

Multiply x and x to get x^{2}.

$$34.8=x^{2}\times 3$$

Swap sides so that all variable terms are on the left hand side.

$$x^{2}\times 3=34.8$$

Divide both sides by 3.

$$x^{2}=\frac{34.8}{3}$$

Expand \frac{34.8}{3} by multiplying both numerator and the denominator by 10.

$$x^{2}=\frac{348}{30}$$

Reduce the fraction \frac{348}{30} to lowest terms by extracting and canceling out 6.

$$x^{2}=\frac{58}{5}$$

Take the square root of both sides of the equation.

$$x=\frac{\sqrt{290}}{5} x=-\frac{\sqrt{290}}{5}$$

Steps Using the Quadratic Formula

Multiply x and x to get x^{2}.

$$34.8=x^{2}\times 3$$

Swap sides so that all variable terms are on the left hand side.

$$x^{2}\times 3=34.8$$

Subtract 34.8 from both sides.

$$x^{2}\times 3-34.8=0$$

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.

$$3x^{2}-34.8=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 3 for a, 0 for b, and -34.8 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 3\left(-34.8\right)}}{2\times 3}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 3\left(-34.8\right)}}{2\times 3}$$

Multiply -4 times 3.

$$x=\frac{0±\sqrt{-12\left(-34.8\right)}}{2\times 3}$$

Multiply -12 times -34.8.

$$x=\frac{0±\sqrt{417.6}}{2\times 3}$$

Take the square root of 417.6.

$$x=\frac{0±\frac{6\sqrt{290}}{5}}{2\times 3}$$

Multiply 2 times 3.

$$x=\frac{0±\frac{6\sqrt{290}}{5}}{6}$$

Now solve the equation x=\frac{0±\frac{6\sqrt{290}}{5}}{6} when ± is plus.

$$x=\frac{\sqrt{290}}{5}$$

Now solve the equation x=\frac{0±\frac{6\sqrt{290}}{5}}{6} when ± is minus.

$$x=-\frac{\sqrt{290}}{5}$$

The equation is now solved.

$$x=\frac{\sqrt{290}}{5} x=-\frac{\sqrt{290}}{5}$$