Solve 5x^2-4=1900

$$5 x ^ { 2 } - 4 = 1900$$

Solve for x

$$x = \frac{4 \sqrt{595}}{5} \approx 19.514097468$$

$$x = -\frac{4 \sqrt{595}}{5} \approx -19.514097468$$

Steps by Finding Square Root

Add 4 to both sides.

$$5x^{2}=1900+4$$

Add 1900 and 4 to get 1904.

$$5x^{2}=1904$$

Divide both sides by 5.

$$x^{2}=\frac{1904}{5}$$

Take the square root of both sides of the equation.

$$x=\frac{4\sqrt{595}}{5} x=-\frac{4\sqrt{595}}{5}$$

Steps Using the Quadratic Formula

Subtract 1900 from both sides.

$$5x^{2}-4-1900=0$$

Subtract 1900 from -4 to get -1904.

$$5x^{2}-1904=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 5 for a, 0 for b, and -1904 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 5\left(-1904\right)}}{2\times 5}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 5\left(-1904\right)}}{2\times 5}$$

Multiply -4 times 5.

$$x=\frac{0±\sqrt{-20\left(-1904\right)}}{2\times 5}$$

Multiply -20 times -1904.

$$x=\frac{0±\sqrt{38080}}{2\times 5}$$

Take the square root of 38080.

$$x=\frac{0±8\sqrt{595}}{2\times 5}$$

Multiply 2 times 5.

$$x=\frac{0±8\sqrt{595}}{10}$$

Now solve the equation x=\frac{0±8\sqrt{595}}{10} when ± is plus.

$$x=\frac{4\sqrt{595}}{5}$$

Now solve the equation x=\frac{0±8\sqrt{595}}{10} when ± is minus.

$$x=-\frac{4\sqrt{595}}{5}$$

The equation is now solved.

$$x=\frac{4\sqrt{595}}{5} x=-\frac{4\sqrt{595}}{5}$$