Solve 2x^2+3.2=6

$$2 { x }^{ 2 } +3.2=6$$

Solve for x

$$x = \frac{\sqrt{35}}{5} \approx 1.183215957$$

$$x = -\frac{\sqrt{35}}{5} \approx -1.183215957$$

Steps by Finding Square Root

Subtract 3.2 from both sides.

$$2x^{2}=6-3.2$$

Subtract 3.2 from 6 to get 2.8.

$$2x^{2}=2.8$$

Divide both sides by 2.

$$x^{2}=\frac{2.8}{2}$$

Expand \frac{2.8}{2} by multiplying both numerator and the denominator by 10.

$$x^{2}=\frac{28}{20}$$

Reduce the fraction \frac{28}{20} to lowest terms by extracting and canceling out 4.

$$x^{2}=\frac{7}{5}$$

Take the square root of both sides of the equation.

$$x=\frac{\sqrt{35}}{5} x=-\frac{\sqrt{35}}{5}$$

Steps Using the Quadratic Formula

Subtract 6 from both sides.

$$2x^{2}+3.2-6=0$$

Subtract 6 from 3.2 to get -2.8.

$$2x^{2}-2.8=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 2 for a, 0 for b, and -2.8 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 2\left(-2.8\right)}}{2\times 2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 2\left(-2.8\right)}}{2\times 2}$$

Multiply -4 times 2.

$$x=\frac{0±\sqrt{-8\left(-2.8\right)}}{2\times 2}$$

Multiply -8 times -2.8.

$$x=\frac{0±\sqrt{22.4}}{2\times 2}$$

Take the square root of 22.4.

$$x=\frac{0±\frac{4\sqrt{35}}{5}}{2\times 2}$$

Multiply 2 times 2.

$$x=\frac{0±\frac{4\sqrt{35}}{5}}{4}$$

Now solve the equation x=\frac{0±\frac{4\sqrt{35}}{5}}{4} when ± is plus.

$$x=\frac{\sqrt{35}}{5}$$

Now solve the equation x=\frac{0±\frac{4\sqrt{35}}{5}}{4} when ± is minus.

$$x=-\frac{\sqrt{35}}{5}$$

The equation is now solved.

$$x=\frac{\sqrt{35}}{5} x=-\frac{\sqrt{35}}{5}$$