Solve 2x^2+3=27.3

$$2 x ^ { 2 } + 3 = 27.3$$

Solve for x

$$x = \frac{9 \sqrt{15}}{10} \approx 3.485685012$$

$$x = -\frac{9 \sqrt{15}}{10} \approx -3.485685012$$

Steps by Finding Square Root

Subtract 3 from both sides.

$$2x^{2}=27.3-3$$

Subtract 3 from 27.3 to get 24.3.

$$2x^{2}=24.3$$

Divide both sides by 2.

$$x^{2}=\frac{24.3}{2}$$

Expand \frac{24.3}{2} by multiplying both numerator and the denominator by 10.

$$x^{2}=\frac{243}{20}$$

Take the square root of both sides of the equation.

$$x=\frac{9\sqrt{15}}{10} x=-\frac{9\sqrt{15}}{10}$$

Steps Using the Quadratic Formula

Subtract 27.3 from both sides.

$$2x^{2}+3-27.3=0$$

Subtract 27.3 from 3 to get -24.3.

$$2x^{2}-24.3=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 2 for a, 0 for b, and -24.3 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 2\left(-24.3\right)}}{2\times 2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 2\left(-24.3\right)}}{2\times 2}$$

Multiply -4 times 2.

$$x=\frac{0±\sqrt{-8\left(-24.3\right)}}{2\times 2}$$

Multiply -8 times -24.3.

$$x=\frac{0±\sqrt{194.4}}{2\times 2}$$

Take the square root of 194.4.

$$x=\frac{0±\frac{18\sqrt{15}}{5}}{2\times 2}$$

Multiply 2 times 2.

$$x=\frac{0±\frac{18\sqrt{15}}{5}}{4}$$

Now solve the equation x=\frac{0±\frac{18\sqrt{15}}{5}}{4} when ± is plus.

$$x=\frac{9\sqrt{15}}{10}$$

Now solve the equation x=\frac{0±\frac{18\sqrt{15}}{5}}{4} when ± is minus.

$$x=-\frac{9\sqrt{15}}{10}$$

The equation is now solved.

$$x=\frac{9\sqrt{15}}{10} x=-\frac{9\sqrt{15}}{10}$$