Solve 203x^2+9=45

$$203 x ^ { 2 } + 9 = 45$$

Solve for x

$$x=\frac{6\sqrt{203}}{203}\approx 0.421117444$$

$$x=-\frac{6\sqrt{203}}{203}\approx -0.421117444$$

Steps by Finding Square Root

Subtract 9 from both sides.

$$203x^{2}=45-9$$

Subtract 9 from 45 to get 36.

$$203x^{2}=36$$

Divide both sides by 203.

$$x^{2}=\frac{36}{203}$$

Take the square root of both sides of the equation.

$$x=\frac{6\sqrt{203}}{203} x=-\frac{6\sqrt{203}}{203}$$

Steps Using the Quadratic Formula

Subtract 45 from both sides.

$$203x^{2}+9-45=0$$

Subtract 45 from 9 to get -36.

$$203x^{2}-36=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 203 for a, 0 for b, and -36 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 203\left(-36\right)}}{2\times 203}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 203\left(-36\right)}}{2\times 203}$$

Multiply -4 times 203.

$$x=\frac{0±\sqrt{-812\left(-36\right)}}{2\times 203}$$

Multiply -812 times -36.

$$x=\frac{0±\sqrt{29232}}{2\times 203}$$

Take the square root of 29232.

$$x=\frac{0±12\sqrt{203}}{2\times 203}$$

Multiply 2 times 203.

$$x=\frac{0±12\sqrt{203}}{406}$$

Now solve the equation x=\frac{0±12\sqrt{203}}{406} when ± is plus.

$$x=\frac{6\sqrt{203}}{203}$$

Now solve the equation x=\frac{0±12\sqrt{203}}{406} when ± is minus.

$$x=-\frac{6\sqrt{203}}{203}$$

The equation is now solved.

$$x=\frac{6\sqrt{203}}{203} x=-\frac{6\sqrt{203}}{203}$$