Solve (7x+3x)+10x=100/x

$$( 7 x + 3 x ) + 10 x = \frac { 100 } { x }$$

Solve for x

$$x=\sqrt{5}\approx 2.236067977$$

$$x=-\sqrt{5}\approx -2.236067977$$

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 x.

$$7xx+3xx+10xx=100$$

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

$$7x^{2}+3xx+10xx=100$$

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

$$7x^{2}+3x^{2}+10xx=100$$

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

$$7x^{2}+3x^{2}+10x^{2}=100$$

Combine 7x^{2} and 3x^{2} to get 10x^{2}.

$$10x^{2}+10x^{2}=100$$

Combine 10x^{2} and 10x^{2} to get 20x^{2}.

$$20x^{2}=100$$

Divide both sides by 20.

$$x^{2}=\frac{100}{20}$$

Divide 100 by 20 to get 5.

$$x^{2}=5$$

Take the square root of both sides of the equation.

$$x=\sqrt{5} x=-\sqrt{5}$$

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 x.

$$7xx+3xx+10xx=100$$

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

$$7x^{2}+3xx+10xx=100$$

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

$$7x^{2}+3x^{2}+10xx=100$$

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

$$7x^{2}+3x^{2}+10x^{2}=100$$

Combine 7x^{2} and 3x^{2} to get 10x^{2}.

$$10x^{2}+10x^{2}=100$$

Combine 10x^{2} and 10x^{2} to get 20x^{2}.

$$20x^{2}=100$$

Subtract 100 from both sides.

$$20x^{2}-100=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 20 for a, 0 for b, and -100 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 20\left(-100\right)}}{2\times 20}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 20\left(-100\right)}}{2\times 20}$$

Multiply -4 times 20.

$$x=\frac{0±\sqrt{-80\left(-100\right)}}{2\times 20}$$

Multiply -80 times -100.

$$x=\frac{0±\sqrt{8000}}{2\times 20}$$

Take the square root of 8000.

$$x=\frac{0±40\sqrt{5}}{2\times 20}$$

Multiply 2 times 20.

$$x=\frac{0±40\sqrt{5}}{40}$$

Now solve the equation x=\frac{0±40\sqrt{5}}{40} when ± is plus.

$$x=\sqrt{5}$$

Now solve the equation x=\frac{0±40\sqrt{5}}{40} when ± is minus.

$$x=-\sqrt{5}$$

The equation is now solved.

$$x=\sqrt{5} x=-\sqrt{5}$$