Solve 1/2x+x=51/x

$$\frac{ 1 }{ 2 } x+x = \frac{ 51 }{ x }$$

Solve for x

$$x=\sqrt{34}\approx 5.830951895$$

$$x=-\sqrt{34}\approx -5.830951895$$

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 2x, the least common multiple of 2,x.

$$\frac{1}{2}x\times 2x+2xx=2\times 51$$

Cancel out 2 and 2.

$$xx+2xx=2\times 51$$

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

$$x^{2}+2xx=2\times 51$$

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

$$x^{2}+2x^{2}=2\times 51$$

Combine x^{2} and 2x^{2} to get 3x^{2}.

$$3x^{2}=2\times 51$$

Multiply 2 and 51 to get 102.

$$3x^{2}=102$$

Divide both sides by 3.

$$x^{2}=\frac{102}{3}$$

Divide 102 by 3 to get 34.

$$x^{2}=34$$

Take the square root of both sides of the equation.

$$x=\sqrt{34} x=-\sqrt{34}$$

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 2x, the least common multiple of 2,x.

$$\frac{1}{2}x\times 2x+2xx=2\times 51$$

Cancel out 2 and 2.

$$xx+2xx=2\times 51$$

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

$$x^{2}+2xx=2\times 51$$

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

$$x^{2}+2x^{2}=2\times 51$$

Combine x^{2} and 2x^{2} to get 3x^{2}.

$$3x^{2}=2\times 51$$

Multiply 2 and 51 to get 102.

$$3x^{2}=102$$

Subtract 102 from both sides.

$$3x^{2}-102=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 3 for a, 0 for b, and -102 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 3\left(-102\right)}}{2\times 3}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 3\left(-102\right)}}{2\times 3}$$

Multiply -4 times 3.

$$x=\frac{0±\sqrt{-12\left(-102\right)}}{2\times 3}$$

Multiply -12 times -102.

$$x=\frac{0±\sqrt{1224}}{2\times 3}$$

Take the square root of 1224.

$$x=\frac{0±6\sqrt{34}}{2\times 3}$$

Multiply 2 times 3.

$$x=\frac{0±6\sqrt{34}}{6}$$

Now solve the equation x=\frac{0±6\sqrt{34}}{6} when ± is plus.

$$x=\sqrt{34}$$

Now solve the equation x=\frac{0±6\sqrt{34}}{6} when ± is minus.

$$x=-\sqrt{34}$$

The equation is now solved.

$$x=\sqrt{34} x=-\sqrt{34}$$