Solve 600-5x-0.01x^2=0

$$600 - 5 x - 0.01 x ^ { 2 } = 0$$

Solve for x

$$x=-600$$

$$x=100$$

Steps Using the Quadratic Formula

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.

$$-0.01x^{2}-5x+600=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -0.01 for a, -5 for b, and 600 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-5\right)±\sqrt{\left(-5\right)^{2}-4\left(-0.01\right)\times 600}}{2\left(-0.01\right)}$$

Square -5.

$$x=\frac{-\left(-5\right)±\sqrt{25-4\left(-0.01\right)\times 600}}{2\left(-0.01\right)}$$

Multiply -4 times -0.01.

$$x=\frac{-\left(-5\right)±\sqrt{25+0.04\times 600}}{2\left(-0.01\right)}$$

Multiply 0.04 times 600.

$$x=\frac{-\left(-5\right)±\sqrt{25+24}}{2\left(-0.01\right)}$$

Add 25 to 24.

$$x=\frac{-\left(-5\right)±\sqrt{49}}{2\left(-0.01\right)}$$

Take the square root of 49.

$$x=\frac{-\left(-5\right)±7}{2\left(-0.01\right)}$$

The opposite of -5 is 5.

$$x=\frac{5±7}{2\left(-0.01\right)}$$

Multiply 2 times -0.01.

$$x=\frac{5±7}{-0.02}$$

Now solve the equation x=\frac{5±7}{-0.02} when ± is plus. Add 5 to 7.

$$x=\frac{12}{-0.02}$$

Divide 12 by -0.02 by multiplying 12 by the reciprocal of -0.02.

$$x=-600$$

Now solve the equation x=\frac{5±7}{-0.02} when ± is minus. Subtract 7 from 5.

$$x=-\frac{2}{-0.02}$$

Divide -2 by -0.02 by multiplying -2 by the reciprocal of -0.02.

$$x=100$$

The equation is now solved.

$$x=-600 x=100$$

Steps for Completing the Square

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.

$$-0.01x^{2}-5x+600=0$$

Subtract 600 from both sides of the equation.

$$-0.01x^{2}-5x+600-600=-600$$

Subtracting 600 from itself leaves 0.

$$-0.01x^{2}-5x=-600$$

Multiply both sides by -100.

$$\frac{-0.01x^{2}-5x}{-0.01}=-\frac{600}{-0.01}$$

Dividing by -0.01 undoes the multiplication by -0.01.

$$x^{2}+\left(-\frac{5}{-0.01}\right)x=-\frac{600}{-0.01}$$

Divide -5 by -0.01 by multiplying -5 by the reciprocal of -0.01.

$$x^{2}+500x=-\frac{600}{-0.01}$$

Divide -600 by -0.01 by multiplying -600 by the reciprocal of -0.01.

$$x^{2}+500x=60000$$

Divide 500, the coefficient of the x term, by 2 to get 250. Then add the square of 250 to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}+500x+250^{2}=60000+250^{2}$$

Square 250.

$$x^{2}+500x+62500=60000+62500$$

Add 60000 to 62500.

$$x^{2}+500x+62500=122500$$

Factor x^{2}+500x+62500. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(x+250\right)^{2}=122500$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x+250\right)^{2}}=\sqrt{122500}$$

Simplify.

$$x+250=350 x+250=-350$$

Subtract 250 from both sides of the equation.

$$x=100 x=-600$$