Solve (x/4)^2+64x^2=34

$$( \frac { x } { 4 } ) ^ { 2 } + 64 x ^ { 2 } = 34$$

Solve for x

$$x=\frac{4\sqrt{1394}}{205}\approx 0.728513354$$

$$x=-\frac{4\sqrt{1394}}{205}\approx -0.728513354$$

Steps by Finding Square Root

To raise \frac{x}{4} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{x^{2}}{4^{2}}+64x^{2}=34$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 64x^{2} times \frac{4^{2}}{4^{2}}.

$$\frac{x^{2}}{4^{2}}+\frac{64x^{2}\times 4^{2}}{4^{2}}=34$$

Since \frac{x^{2}}{4^{2}} and \frac{64x^{2}\times 4^{2}}{4^{2}} have the same denominator, add them by adding their numerators.

$$\frac{x^{2}+64x^{2}\times 4^{2}}{4^{2}}=34$$

Do the multiplications in x^{2}+64x^{2}\times 4^{2}.

$$\frac{x^{2}+1024x^{2}}{4^{2}}=34$$

Combine like terms in x^{2}+1024x^{2}.

$$\frac{1025x^{2}}{4^{2}}=34$$

Calculate 4 to the power of 2 and get 16.

$$\frac{1025x^{2}}{16}=34$$

Multiply both sides by 16.

$$1025x^{2}=34\times 16$$

Multiply 34 and 16 to get 544.

$$1025x^{2}=544$$

Divide both sides by 1025.

$$x^{2}=\frac{544}{1025}$$

Take the square root of both sides of the equation.

$$x=\frac{4\sqrt{1394}}{205} x=-\frac{4\sqrt{1394}}{205}$$

Steps Using the Quadratic Formula

To raise \frac{x}{4} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{x^{2}}{4^{2}}+64x^{2}=34$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 64x^{2} times \frac{4^{2}}{4^{2}}.

$$\frac{x^{2}}{4^{2}}+\frac{64x^{2}\times 4^{2}}{4^{2}}=34$$

Since \frac{x^{2}}{4^{2}} and \frac{64x^{2}\times 4^{2}}{4^{2}} have the same denominator, add them by adding their numerators.

$$\frac{x^{2}+64x^{2}\times 4^{2}}{4^{2}}=34$$

Do the multiplications in x^{2}+64x^{2}\times 4^{2}.

$$\frac{x^{2}+1024x^{2}}{4^{2}}=34$$

Combine like terms in x^{2}+1024x^{2}.

$$\frac{1025x^{2}}{4^{2}}=34$$

Calculate 4 to the power of 2 and get 16.

$$\frac{1025x^{2}}{16}=34$$

Subtract 34 from both sides.

$$\frac{1025x^{2}}{16}-34=0$$

Multiply both sides of the equation by 16.

$$1025x^{2}-544=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1025 for a, 0 for b, and -544 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 1025\left(-544\right)}}{2\times 1025}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 1025\left(-544\right)}}{2\times 1025}$$

Multiply -4 times 1025.

$$x=\frac{0±\sqrt{-4100\left(-544\right)}}{2\times 1025}$$

Multiply -4100 times -544.

$$x=\frac{0±\sqrt{2230400}}{2\times 1025}$$

Take the square root of 2230400.

$$x=\frac{0±40\sqrt{1394}}{2\times 1025}$$

Multiply 2 times 1025.

$$x=\frac{0±40\sqrt{1394}}{2050}$$

Now solve the equation x=\frac{0±40\sqrt{1394}}{2050} when ± is plus.

$$x=\frac{4\sqrt{1394}}{205}$$

Now solve the equation x=\frac{0±40\sqrt{1394}}{2050} when ± is minus.

$$x=-\frac{4\sqrt{1394}}{205}$$

The equation is now solved.

$$x=\frac{4\sqrt{1394}}{205} x=-\frac{4\sqrt{1394}}{205}$$