Solve left(2560xright)^2+left(1080xright)^2=29^2

$${ \left(2560x \right) }^{ 2 } + { \left(1080x \right) }^{ 2 } = { 29 }^{ 2 }$$

Solve for x

$$x=\frac{29\sqrt{193}}{38600}\approx 0.010437328$$

$$x=-\frac{29\sqrt{193}}{38600}\approx -0.010437328$$

Steps by Finding Square Root

Expand \left(2560x\right)^{2}.

$$2560^{2}x^{2}+\left(1080x\right)^{2}=29^{2}$$

Calculate 2560 to the power of 2 and get 6553600.

$$6553600x^{2}+\left(1080x\right)^{2}=29^{2}$$

Expand \left(1080x\right)^{2}.

$$6553600x^{2}+1080^{2}x^{2}=29^{2}$$

Calculate 1080 to the power of 2 and get 1166400.

$$6553600x^{2}+1166400x^{2}=29^{2}$$

Combine 6553600x^{2} and 1166400x^{2} to get 7720000x^{2}.

$$7720000x^{2}=29^{2}$$

Calculate 29 to the power of 2 and get 841.

$$7720000x^{2}=841$$

Divide both sides by 7720000.

$$x^{2}=\frac{841}{7720000}$$

Take the square root of both sides of the equation.

$$x=\frac{29\sqrt{193}}{38600} x=-\frac{29\sqrt{193}}{38600}$$

Steps Using the Quadratic Formula

Expand \left(2560x\right)^{2}.

$$2560^{2}x^{2}+\left(1080x\right)^{2}=29^{2}$$

Calculate 2560 to the power of 2 and get 6553600.

$$6553600x^{2}+\left(1080x\right)^{2}=29^{2}$$

Expand \left(1080x\right)^{2}.

$$6553600x^{2}+1080^{2}x^{2}=29^{2}$$

Calculate 1080 to the power of 2 and get 1166400.

$$6553600x^{2}+1166400x^{2}=29^{2}$$

Combine 6553600x^{2} and 1166400x^{2} to get 7720000x^{2}.

$$7720000x^{2}=29^{2}$$

Calculate 29 to the power of 2 and get 841.

$$7720000x^{2}=841$$

Subtract 841 from both sides.

$$7720000x^{2}-841=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 7720000 for a, 0 for b, and -841 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 7720000\left(-841\right)}}{2\times 7720000}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 7720000\left(-841\right)}}{2\times 7720000}$$

Multiply -4 times 7720000.

$$x=\frac{0±\sqrt{-30880000\left(-841\right)}}{2\times 7720000}$$

Multiply -30880000 times -841.

$$x=\frac{0±\sqrt{25970080000}}{2\times 7720000}$$

Take the square root of 25970080000.

$$x=\frac{0±11600\sqrt{193}}{2\times 7720000}$$

Multiply 2 times 7720000.

$$x=\frac{0±11600\sqrt{193}}{15440000}$$

Now solve the equation x=\frac{0±11600\sqrt{193}}{15440000} when ± is plus.

$$x=\frac{29\sqrt{193}}{38600}$$

Now solve the equation x=\frac{0±11600\sqrt{193}}{15440000} when ± is minus.

$$x=-\frac{29\sqrt{193}}{38600}$$

The equation is now solved.

$$x=\frac{29\sqrt{193}}{38600} x=-\frac{29\sqrt{193}}{38600}$$