Solve 5x^2+3=373

$$5 x ^ { 2 } + 3 = 373$$

Solve for x

$$x=\sqrt{74}\approx 8.602325267$$

$$x=-\sqrt{74}\approx -8.602325267$$

Steps by Finding Square Root

Subtract 3 from both sides.

$$5x^{2}=373-3$$

Subtract 3 from 373 to get 370.

$$5x^{2}=370$$

Divide both sides by 5.

$$x^{2}=\frac{370}{5}$$

Divide 370 by 5 to get 74.

$$x^{2}=74$$

Take the square root of both sides of the equation.

$$x=\sqrt{74} x=-\sqrt{74}$$

Steps Using the Quadratic Formula

Subtract 373 from both sides.

$$5x^{2}+3-373=0$$

Subtract 373 from 3 to get -370.

$$5x^{2}-370=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 5 for a, 0 for b, and -370 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 5\left(-370\right)}}{2\times 5}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 5\left(-370\right)}}{2\times 5}$$

Multiply -4 times 5.

$$x=\frac{0±\sqrt{-20\left(-370\right)}}{2\times 5}$$

Multiply -20 times -370.

$$x=\frac{0±\sqrt{7400}}{2\times 5}$$

Take the square root of 7400.

$$x=\frac{0±10\sqrt{74}}{2\times 5}$$

Multiply 2 times 5.

$$x=\frac{0±10\sqrt{74}}{10}$$

Now solve the equation x=\frac{0±10\sqrt{74}}{10} when ± is plus.

$$x=\sqrt{74}$$

Now solve the equation x=\frac{0±10\sqrt{74}}{10} when ± is minus.

$$x=-\sqrt{74}$$

The equation is now solved.

$$x=\sqrt{74} x=-\sqrt{74}$$