Solve 1/2x+3/5x=1/2x

$$\frac { 1 } { 2 } x + \frac { 3 } { 5 } x = \frac { 1 } { 2 x }$$

Solve for x

$$x=\frac{\sqrt{55}}{11}\approx 0.674199862$$

$$x=-\frac{\sqrt{55}}{11}\approx -0.674199862$$

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 2,5,2x.

$$\frac{1}{2}x\times 10x+\frac{3}{5}x\times 10x=5$$

Multiply \frac{1}{2} and 10 to get 5.

$$5xx+\frac{3}{5}x\times 10x=5$$

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

$$5x^{2}+\frac{3}{5}x\times 10x=5$$

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

$$5x^{2}+\frac{3}{5}x^{2}\times 10=5$$

Multiply \frac{3}{5} and 10 to get 6.

$$5x^{2}+6x^{2}=5$$

Combine 5x^{2} and 6x^{2} to get 11x^{2}.

$$11x^{2}=5$$

Divide both sides by 11.

$$x^{2}=\frac{5}{11}$$

Take the square root of both sides of the equation.

$$x=\frac{\sqrt{55}}{11} x=-\frac{\sqrt{55}}{11}$$

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 2,5,2x.

$$\frac{1}{2}x\times 10x+\frac{3}{5}x\times 10x=5$$

Multiply \frac{1}{2} and 10 to get 5.

$$5xx+\frac{3}{5}x\times 10x=5$$

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

$$5x^{2}+\frac{3}{5}x\times 10x=5$$

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

$$5x^{2}+\frac{3}{5}x^{2}\times 10=5$$

Multiply \frac{3}{5} and 10 to get 6.

$$5x^{2}+6x^{2}=5$$

Combine 5x^{2} and 6x^{2} to get 11x^{2}.

$$11x^{2}=5$$

Subtract 5 from both sides.

$$11x^{2}-5=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 11 for a, 0 for b, and -5 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 11\left(-5\right)}}{2\times 11}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 11\left(-5\right)}}{2\times 11}$$

Multiply -4 times 11.

$$x=\frac{0±\sqrt{-44\left(-5\right)}}{2\times 11}$$

Multiply -44 times -5.

$$x=\frac{0±\sqrt{220}}{2\times 11}$$

Take the square root of 220.

$$x=\frac{0±2\sqrt{55}}{2\times 11}$$

Multiply 2 times 11.

$$x=\frac{0±2\sqrt{55}}{22}$$

Now solve the equation x=\frac{0±2\sqrt{55}}{22} when ± is plus.

$$x=\frac{\sqrt{55}}{11}$$

Now solve the equation x=\frac{0±2\sqrt{55}}{22} when ± is minus.

$$x=-\frac{\sqrt{55}}{11}$$

The equation is now solved.

$$x=\frac{\sqrt{55}}{11} x=-\frac{\sqrt{55}}{11}$$