Solve -50/x+10-0.02x=10-0.04x

$$- \frac{ 50 }{ x } +10-0.02x=10-0.04x$$

Solve for x

$$x=-50$$

$$x=50$$

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.

$$-50+x\times 10-0.02xx=x\times 10-0.04xx$$

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

$$-50+x\times 10-0.02x^{2}=x\times 10-0.04xx$$

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

$$-50+x\times 10-0.02x^{2}=x\times 10-0.04x^{2}$$

Subtract x\times 10 from both sides.

$$-50+x\times 10-0.02x^{2}-x\times 10=-0.04x^{2}$$

Combine x\times 10 and -x\times 10 to get 0.

$$-50-0.02x^{2}=-0.04x^{2}$$

Add 0.04x^{2} to both sides.

$$-50-0.02x^{2}+0.04x^{2}=0$$

Combine -0.02x^{2} and 0.04x^{2} to get 0.02x^{2}.

$$-50+0.02x^{2}=0$$

Add 50 to both sides. Anything plus zero gives itself.

$$0.02x^{2}=50$$

Divide both sides by 0.02.

$$x^{2}=\frac{50}{0.02}$$

Expand \frac{50}{0.02} by multiplying both numerator and the denominator by 100.

$$x^{2}=\frac{5000}{2}$$

Divide 5000 by 2 to get 2500.

$$x^{2}=2500$$

Take the square root of both sides of the equation.

$$x=50 x=-50$$

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.

$$-50+x\times 10-0.02xx=x\times 10-0.04xx$$

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

$$-50+x\times 10-0.02x^{2}=x\times 10-0.04xx$$

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

$$-50+x\times 10-0.02x^{2}=x\times 10-0.04x^{2}$$

Subtract x\times 10 from both sides.

$$-50+x\times 10-0.02x^{2}-x\times 10=-0.04x^{2}$$

Combine x\times 10 and -x\times 10 to get 0.

$$-50-0.02x^{2}=-0.04x^{2}$$

Add 0.04x^{2} to both sides.

$$-50-0.02x^{2}+0.04x^{2}=0$$

Combine -0.02x^{2} and 0.04x^{2} to get 0.02x^{2}.

$$-50+0.02x^{2}=0$$

Quadratic equations like this one, with an x^{2} term but no x term, can still be solved using the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}, once they are put in standard form: ax^{2}+bx+c=0.

$$0.02x^{2}-50=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 0.02 for a, 0 for b, and -50 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 0.02\left(-50\right)}}{2\times 0.02}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 0.02\left(-50\right)}}{2\times 0.02}$$

Multiply -4 times 0.02.

$$x=\frac{0±\sqrt{-0.08\left(-50\right)}}{2\times 0.02}$$

Multiply -0.08 times -50.

$$x=\frac{0±\sqrt{4}}{2\times 0.02}$$

Take the square root of 4.

$$x=\frac{0±2}{2\times 0.02}$$

Multiply 2 times 0.02.

$$x=\frac{0±2}{0.04}$$

Now solve the equation x=\frac{0±2}{0.04} when ± is plus. Divide 2 by 0.04 by multiplying 2 by the reciprocal of 0.04.

$$x=50$$

Now solve the equation x=\frac{0±2}{0.04} when ± is minus. Divide -2 by 0.04 by multiplying -2 by the reciprocal of 0.04.

$$x=-50$$

The equation is now solved.

$$x=50 x=-50$$