Solve x/10=17/x

$$\frac{ x }{ 10 } = \frac{ 17 }{ x }$$

Solve for x

$$x=\sqrt{170}\approx 13.03840481$$

$$x=-\sqrt{170}\approx -13.03840481$$

Steps by Finding Square Root

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 10x, the least common multiple of 10,x.

$$xx=10\times 17$$

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

$$x^{2}=10\times 17$$

Multiply 10 and 17 to get 170.

$$x^{2}=170$$

Take the square root of both sides of the equation.

$$x=\sqrt{170} x=-\sqrt{170}$$

Steps Using the Quadratic Formula

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 10x, the least common multiple of 10,x.

$$xx=10\times 17$$

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

$$x^{2}=10\times 17$$

Multiply 10 and 17 to get 170.

$$x^{2}=170$$

Subtract 170 from both sides.

$$x^{2}-170=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -170 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-170\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-170\right)}}{2}$$

Multiply -4 times -170.

$$x=\frac{0±\sqrt{680}}{2}$$

Take the square root of 680.

$$x=\frac{0±2\sqrt{170}}{2}$$

Now solve the equation x=\frac{0±2\sqrt{170}}{2} when ± is plus.

$$x=\sqrt{170}$$

Now solve the equation x=\frac{0±2\sqrt{170}}{2} when ± is minus.

$$x=-\sqrt{170}$$

The equation is now solved.

$$x=\sqrt{170} x=-\sqrt{170}$$