Solve 3600-4x^2=900

$$3600 - 4 x ^ { 2 } = 900$$

Solve for x

$$x=15\sqrt{3}\approx 25.980762114$$

$$x=-15\sqrt{3}\approx -25.980762114$$

Steps by Finding Square Root

Subtract 3600 from both sides.

$$-4x^{2}=900-3600$$

Subtract 3600 from 900 to get -2700.

$$-4x^{2}=-2700$$

Divide both sides by -4.

$$x^{2}=\frac{-2700}{-4}$$

Divide -2700 by -4 to get 675.

$$x^{2}=675$$

Take the square root of both sides of the equation.

$$x=15\sqrt{3} x=-15\sqrt{3}$$

Steps Using the Quadratic Formula

Subtract 900 from both sides.

$$3600-4x^{2}-900=0$$

Subtract 900 from 3600 to get 2700.

$$2700-4x^{2}=0$$

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.

$$-4x^{2}+2700=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -4 for a, 0 for b, and 2700 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-4\right)\times 2700}}{2\left(-4\right)}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-4\right)\times 2700}}{2\left(-4\right)}$$

Multiply -4 times -4.

$$x=\frac{0±\sqrt{16\times 2700}}{2\left(-4\right)}$$

Multiply 16 times 2700.

$$x=\frac{0±\sqrt{43200}}{2\left(-4\right)}$$

Take the square root of 43200.

$$x=\frac{0±120\sqrt{3}}{2\left(-4\right)}$$

Multiply 2 times -4.

$$x=\frac{0±120\sqrt{3}}{-8}$$

Now solve the equation x=\frac{0±120\sqrt{3}}{-8} when ± is plus.

$$x=-15\sqrt{3}$$

Now solve the equation x=\frac{0±120\sqrt{3}}{-8} when ± is minus.

$$x=15\sqrt{3}$$

The equation is now solved.

$$x=-15\sqrt{3} x=15\sqrt{3}$$