Solve 8.50=0.08x+50/x

$$8.50=0.08x+ \frac{ 50 }{ x }$$

Solve for x

$$x=6.25$$

$$x=100$$

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.

$$8.5x=0.08xx+50$$

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

$$8.5x=0.08x^{2}+50$$

Subtract 0.08x^{2} from both sides.

$$8.5x-0.08x^{2}=50$$

Subtract 50 from both sides.

$$8.5x-0.08x^{2}-50=0$$

All equations of the form ax^{2}+bx+c=0 can be solved using the quadratic formula: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. The quadratic formula gives two solutions, one when ± is addition and one when it is subtraction.

$$-0.08x^{2}+8.5x-50=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -0.08 for a, 8.5 for b, and -50 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-8.5±\sqrt{8.5^{2}-4\left(-0.08\right)\left(-50\right)}}{2\left(-0.08\right)}$$

Square 8.5 by squaring both the numerator and the denominator of the fraction.

$$x=\frac{-8.5±\sqrt{72.25-4\left(-0.08\right)\left(-50\right)}}{2\left(-0.08\right)}$$

Multiply -4 times -0.08.

$$x=\frac{-8.5±\sqrt{72.25+0.32\left(-50\right)}}{2\left(-0.08\right)}$$

Multiply 0.32 times -50.

$$x=\frac{-8.5±\sqrt{72.25-16}}{2\left(-0.08\right)}$$

Add 72.25 to -16.

$$x=\frac{-8.5±\sqrt{56.25}}{2\left(-0.08\right)}$$

Take the square root of 56.25.

$$x=\frac{-8.5±\frac{15}{2}}{2\left(-0.08\right)}$$

Multiply 2 times -0.08.

$$x=\frac{-8.5±\frac{15}{2}}{-0.16}$$

Now solve the equation x=\frac{-8.5±\frac{15}{2}}{-0.16} when ± is plus. Add -8.5 to \frac{15}{2} by finding a common denominator and adding the numerators. Then reduce the fraction to lowest terms if possible.

$$x=-\frac{1}{-0.16}$$

Divide -1 by -0.16 by multiplying -1 by the reciprocal of -0.16.

$$x=6.25$$

Now solve the equation x=\frac{-8.5±\frac{15}{2}}{-0.16} when ± is minus. Subtract \frac{15}{2} from -8.5 by finding a common denominator and subtracting the numerators. Then reduce the fraction to lowest terms if possible.

$$x=-\frac{16}{-0.16}$$

Divide -16 by -0.16 by multiplying -16 by the reciprocal of -0.16.

$$x=100$$

The equation is now solved.

$$x=6.25 x=100$$

Steps for Completing the Square

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by x.

$$8.5x=0.08xx+50$$

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

$$8.5x=0.08x^{2}+50$$

Subtract 0.08x^{2} from both sides.

$$8.5x-0.08x^{2}=50$$

Quadratic equations such as this one can be solved by completing the square. In order to complete the square, the equation must first be in the form x^{2}+bx=c.

$$-0.08x^{2}+8.5x=50$$

Divide both sides of the equation by -0.08, which is the same as multiplying both sides by the reciprocal of the fraction.

$$\frac{-0.08x^{2}+8.5x}{-0.08}=\frac{50}{-0.08}$$

Dividing by -0.08 undoes the multiplication by -0.08.

$$x^{2}+\frac{8.5}{-0.08}x=\frac{50}{-0.08}$$

Divide 8.5 by -0.08 by multiplying 8.5 by the reciprocal of -0.08.

$$x^{2}-106.25x=\frac{50}{-0.08}$$

Divide 50 by -0.08 by multiplying 50 by the reciprocal of -0.08.

$$x^{2}-106.25x=-625$$

Divide -106.25, the coefficient of the x term, by 2 to get -53.125. Then add the square of -53.125 to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}-106.25x+\left(-53.125\right)^{2}=-625+\left(-53.125\right)^{2}$$

Square -53.125 by squaring both the numerator and the denominator of the fraction.

$$x^{2}-106.25x+2822.265625=-625+2822.265625$$

Add -625 to 2822.265625.

$$x^{2}-106.25x+2822.265625=2197.265625$$

Factor x^{2}-106.25x+2822.265625. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(x-53.125\right)^{2}=2197.265625$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x-53.125\right)^{2}}=\sqrt{2197.265625}$$

Simplify.

$$x-53.125=\frac{375}{8} x-53.125=-\frac{375}{8}$$

Add 53.125 to both sides of the equation.

$$x=100 x=\frac{25}{4}$$