Solve 2*60*x+2*40*x+4x^2=2*2400

$$2 \times 60 \times x+2 \times 40 \times x+4 { x }^{ 2 } =2 \times 2400$$

Solve for x

$$x=5\sqrt{73}-25\approx 17.720018727$$

$$x=-5\sqrt{73}-25\approx -67.720018727$$

Steps Using the Quadratic Formula

Do the multiplications.

$$120x+80x+4x^{2}=2\times 2400$$

Combine 120x and 80x to get 200x.

$$200x+4x^{2}=2\times 2400$$

Multiply 2 and 2400 to get 4800.

$$200x+4x^{2}=4800$$

Subtract 4800 from both sides.

$$200x+4x^{2}-4800=0$$

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.

$$4x^{2}+200x-4800=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 4 for a, 200 for b, and -4800 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-200±\sqrt{200^{2}-4\times 4\left(-4800\right)}}{2\times 4}$$

Square 200.

$$x=\frac{-200±\sqrt{40000-4\times 4\left(-4800\right)}}{2\times 4}$$

Multiply -4 times 4.

$$x=\frac{-200±\sqrt{40000-16\left(-4800\right)}}{2\times 4}$$

Multiply -16 times -4800.

$$x=\frac{-200±\sqrt{40000+76800}}{2\times 4}$$

Add 40000 to 76800.

$$x=\frac{-200±\sqrt{116800}}{2\times 4}$$

Take the square root of 116800.

$$x=\frac{-200±40\sqrt{73}}{2\times 4}$$

Multiply 2 times 4.

$$x=\frac{-200±40\sqrt{73}}{8}$$

Now solve the equation x=\frac{-200±40\sqrt{73}}{8} when ± is plus. Add -200 to 40\sqrt{73}.

$$x=\frac{40\sqrt{73}-200}{8}$$

Divide -200+40\sqrt{73} by 8.

$$x=5\sqrt{73}-25$$

Now solve the equation x=\frac{-200±40\sqrt{73}}{8} when ± is minus. Subtract 40\sqrt{73} from -200.

$$x=\frac{-40\sqrt{73}-200}{8}$$

Divide -200-40\sqrt{73} by 8.

$$x=-5\sqrt{73}-25$$

The equation is now solved.

$$x=5\sqrt{73}-25 x=-5\sqrt{73}-25$$

Steps for Completing the Square

Do the multiplications.

$$120x+80x+4x^{2}=2\times 2400$$

Combine 120x and 80x to get 200x.

$$200x+4x^{2}=2\times 2400$$

Multiply 2 and 2400 to get 4800.

$$200x+4x^{2}=4800$$

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.

$$4x^{2}+200x=4800$$

Divide both sides by 4.

$$\frac{4x^{2}+200x}{4}=\frac{4800}{4}$$

Dividing by 4 undoes the multiplication by 4.

$$x^{2}+\frac{200}{4}x=\frac{4800}{4}$$

Divide 200 by 4.

$$x^{2}+50x=\frac{4800}{4}$$

Divide 4800 by 4.

$$x^{2}+50x=1200$$

Divide 50, the coefficient of the x term, by 2 to get 25. Then add the square of 25 to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}+50x+25^{2}=1200+25^{2}$$

Square 25.

$$x^{2}+50x+625=1200+625$$

Add 1200 to 625.

$$x^{2}+50x+625=1825$$

Factor x^{2}+50x+625. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(x+25\right)^{2}=1825$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x+25\right)^{2}}=\sqrt{1825}$$

Simplify.

$$x+25=5\sqrt{73} x+25=-5\sqrt{73}$$

Subtract 25 from both sides of the equation.

$$x=5\sqrt{73}-25 x=-5\sqrt{73}-25$$