Solve x^2+3sqrt{4}=484

$$x ^ { 2 } + 3 \sqrt { 4 } = 484$$

Solve for x

$$x=\sqrt{478}\approx 21.863211109$$

$$x=-\sqrt{478}\approx -21.863211109$$

Steps by Finding Square Root

Calculate the square root of 4 and get 2.

$$x^{2}+3\times 2=484$$

Multiply 3 and 2 to get 6.

$$x^{2}+6=484$$

Subtract 6 from both sides.

$$x^{2}=484-6$$

Subtract 6 from 484 to get 478.

$$x^{2}=478$$

Take the square root of both sides of the equation.

$$x=\sqrt{478} x=-\sqrt{478}$$

Steps Using the Quadratic Formula

Calculate the square root of 4 and get 2.

$$x^{2}+3\times 2=484$$

Multiply 3 and 2 to get 6.

$$x^{2}+6=484$$

Subtract 484 from both sides.

$$x^{2}+6-484=0$$

Subtract 484 from 6 to get -478.

$$x^{2}-478=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -478 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-478\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-478\right)}}{2}$$

Multiply -4 times -478.

$$x=\frac{0±\sqrt{1912}}{2}$$

Take the square root of 1912.

$$x=\frac{0±2\sqrt{478}}{2}$$

Now solve the equation x=\frac{0±2\sqrt{478}}{2} when ± is plus.

$$x=\sqrt{478}$$

Now solve the equation x=\frac{0±2\sqrt{478}}{2} when ± is minus.

$$x=-\sqrt{478}$$

The equation is now solved.

$$x=\sqrt{478} x=-\sqrt{478}$$