Solve 1/2x+x=51/x | Microsoft Math Solver

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Solve for x

x = 34 \approx 5.830951895

x = - 34 \approx - 5.830951895

Steps by Finding Square Root

Steps Using the Quadratic Formula

Steps by Finding Square Root

\frac{1}{2} x + x = \frac{5 1}{x}

Variable

x

cannot be equal to

0

since division by zero is not defined. Multiply both sides of the equation by

2 x

, the least common multiple of

2, x

.

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

Cancel out

2

and

2

.

x x + 2 x x = 2 \times 51

Multiply

x

and

x

to get

x^{2}

.

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

Multiply

x

and

x

to get

x^{2}

.

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

Combine

x^{2}

and

2 x^{2}

to get

3 x^{2}

.

3 x^{2} = 2 \times 51

Multiply

2

and

51

to get

102

.

3 x^{2} = 102

Divide both sides by

3

.

x^{2} = \frac{1 0 2}{3}

Divide

102

by

3

to get

34

.

x^{2} = 34

Take the square root of both sides of the equation.

x = 34

x = - 34

Graph

Graph Both Sides in 2D

Graph in 2D

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\frac{1}{2} x + x = \frac{5 1}{x}

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

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.

xx+2xx=2\times 51

Cancel out 2 and 2.

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

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

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

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

3x^{2}=2\times 51

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

3x^{2}=102

Multiply 2 and 51 to get 102.

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

Divide both sides by 3.

x^{2}=34

Divide 102 by 3 to get 34.

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

Take the square root of both sides of the equation.

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

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.

xx+2xx=2\times 51

Cancel out 2 and 2.

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

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

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

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

3x^{2}=2\times 51

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

3x^{2}=102

Multiply 2 and 51 to get 102.

3x^{2}-102=0

Subtract 102 from both sides.

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

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{-4\times 3\left(-102\right)}}{2\times 3}

Square 0.

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

Multiply -4 times 3.

x=\frac{0±\sqrt{1224}}{2\times 3}

Multiply -12 times -102.

x=\frac{0±6\sqrt{34}}{2\times 3}

Take the square root of 1224.

x=\frac{0±6\sqrt{34}}{6}

Multiply 2 times 3.

x=\sqrt{34}

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} x=-\sqrt{34}

The equation is now solved.

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