Solve 280^2=left(81xright)^2+x^2

$${ 280 }^{ 2 } = { \left(81x \right) }^{ 2 } + { x }^{ 2 }$$

Solve for x

$$x = \frac{140 \sqrt{6562}}{3281} \approx 3.456526719$$

$$x = -\frac{140 \sqrt{6562}}{3281} \approx -3.456526719$$

Steps by Finding Square Root

Calculate 280 to the power of 2 and get 78400.

$$78400=\left(81x\right)^{2}+x^{2}$$

Expand \left(81x\right)^{2}.

$$78400=81^{2}x^{2}+x^{2}$$

Calculate 81 to the power of 2 and get 6561.

$$78400=6561x^{2}+x^{2}$$

Combine 6561x^{2} and x^{2} to get 6562x^{2}.

$$78400=6562x^{2}$$

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

$$6562x^{2}=78400$$

Divide both sides by 6562.

$$x^{2}=\frac{78400}{6562}$$

Reduce the fraction \frac{78400}{6562} to lowest terms by extracting and canceling out 2.

$$x^{2}=\frac{39200}{3281}$$

Take the square root of both sides of the equation.

$$x=\frac{140\sqrt{6562}}{3281} x=-\frac{140\sqrt{6562}}{3281}$$

Steps Using the Quadratic Formula

Calculate 280 to the power of 2 and get 78400.

$$78400=\left(81x\right)^{2}+x^{2}$$

Expand \left(81x\right)^{2}.

$$78400=81^{2}x^{2}+x^{2}$$

Calculate 81 to the power of 2 and get 6561.

$$78400=6561x^{2}+x^{2}$$

Combine 6561x^{2} and x^{2} to get 6562x^{2}.

$$78400=6562x^{2}$$

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

$$6562x^{2}=78400$$

Subtract 78400 from both sides.

$$6562x^{2}-78400=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 6562 for a, 0 for b, and -78400 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 6562\left(-78400\right)}}{2\times 6562}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 6562\left(-78400\right)}}{2\times 6562}$$

Multiply -4 times 6562.

$$x=\frac{0±\sqrt{-26248\left(-78400\right)}}{2\times 6562}$$

Multiply -26248 times -78400.

$$x=\frac{0±\sqrt{2057843200}}{2\times 6562}$$

Take the square root of 2057843200.

$$x=\frac{0±560\sqrt{6562}}{2\times 6562}$$

Multiply 2 times 6562.

$$x=\frac{0±560\sqrt{6562}}{13124}$$

Now solve the equation x=\frac{0±560\sqrt{6562}}{13124} when ± is plus.

$$x=\frac{140\sqrt{6562}}{3281}$$

Now solve the equation x=\frac{0±560\sqrt{6562}}{13124} when ± is minus.

$$x=-\frac{140\sqrt{6562}}{3281}$$

The equation is now solved.

$$x=\frac{140\sqrt{6562}}{3281} x=-\frac{140\sqrt{6562}}{3281}$$