Solve -0.8x^2+8x+2400=0

$$-0.8 { x }^{ 2 } +8x+2400 = 0$$

Solve for x

$$x=-50$$

$$x=60$$

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.

$$-0.8x^{2}+8x+2400=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -0.8 for a, 8 for b, and 2400 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-8±\sqrt{8^{2}-4\left(-0.8\right)\times 2400}}{2\left(-0.8\right)}$$

Square 8.

$$x=\frac{-8±\sqrt{64-4\left(-0.8\right)\times 2400}}{2\left(-0.8\right)}$$

Multiply -4 times -0.8.

$$x=\frac{-8±\sqrt{64+3.2\times 2400}}{2\left(-0.8\right)}$$

Multiply 3.2 times 2400.

$$x=\frac{-8±\sqrt{64+7680}}{2\left(-0.8\right)}$$

Add 64 to 7680.

$$x=\frac{-8±\sqrt{7744}}{2\left(-0.8\right)}$$

Take the square root of 7744.

$$x=\frac{-8±88}{2\left(-0.8\right)}$$

Multiply 2 times -0.8.

$$x=\frac{-8±88}{-1.6}$$

Now solve the equation x=\frac{-8±88}{-1.6} when ± is plus. Add -8 to 88.

$$x=\frac{80}{-1.6}$$

Divide 80 by -1.6 by multiplying 80 by the reciprocal of -1.6.

$$x=-50$$

Now solve the equation x=\frac{-8±88}{-1.6} when ± is minus. Subtract 88 from -8.

$$x=-\frac{96}{-1.6}$$

Divide -96 by -1.6 by multiplying -96 by the reciprocal of -1.6.

$$x=60$$

The equation is now solved.

$$x=-50 x=60$$

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.

$$-0.8x^{2}+8x+2400=0$$

Subtract 2400 from both sides of the equation.

$$-0.8x^{2}+8x+2400-2400=-2400$$

Subtracting 2400 from itself leaves 0.

$$-0.8x^{2}+8x=-2400$$

Divide both sides of the equation by -0.8, which is the same as multiplying both sides by the reciprocal of the fraction.

$$\frac{-0.8x^{2}+8x}{-0.8}=-\frac{2400}{-0.8}$$

Dividing by -0.8 undoes the multiplication by -0.8.

$$x^{2}+\frac{8}{-0.8}x=-\frac{2400}{-0.8}$$

Divide 8 by -0.8 by multiplying 8 by the reciprocal of -0.8.

$$x^{2}-10x=-\frac{2400}{-0.8}$$

Divide -2400 by -0.8 by multiplying -2400 by the reciprocal of -0.8.

$$x^{2}-10x=3000$$

Divide -10, the coefficient of the x term, by 2 to get -5. Then add the square of -5 to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}-10x+\left(-5\right)^{2}=3000+\left(-5\right)^{2}$$

Square -5.

$$x^{2}-10x+25=3000+25$$

Add 3000 to 25.

$$x^{2}-10x+25=3025$$

Factor x^{2}-10x+25. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(x-5\right)^{2}=3025$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x-5\right)^{2}}=\sqrt{3025}$$

Simplify.

$$x-5=55 x-5=-55$$

Add 5 to both sides of the equation.

$$x=60 x=-50$$