Solve 199-40*0.24*0.8=2x^2

$$199 - 40 \times 0.24 \times 0.8 = 2 x ^ { 2 }$$

Solve for x

$$x = \frac{\sqrt{9566}}{10} \approx 9.780593029$$

$$x = -\frac{\sqrt{9566}}{10} \approx -9.780593029$$

Steps by Finding Square Root

Multiply 40 and 0.24 to get 9.6.

$$199-9.6\times 0.8=2x^{2}$$

Multiply 9.6 and 0.8 to get 7.68.

$$199-7.68=2x^{2}$$

Subtract 7.68 from 199 to get 191.32.

$$191.32=2x^{2}$$

Swap sides so that all variable terms are on the left hand side.

$$2x^{2}=191.32$$

Divide both sides by 2.

$$x^{2}=\frac{191.32}{2}$$

Expand \frac{191.32}{2} by multiplying both numerator and the denominator by 100.

$$x^{2}=\frac{19132}{200}$$

Reduce the fraction \frac{19132}{200} to lowest terms by extracting and canceling out 4.

$$x^{2}=\frac{4783}{50}$$

Take the square root of both sides of the equation.

$$x=\frac{\sqrt{9566}}{10} x=-\frac{\sqrt{9566}}{10}$$

Steps Using the Quadratic Formula

Multiply 40 and 0.24 to get 9.6.

$$199-9.6\times 0.8=2x^{2}$$

Multiply 9.6 and 0.8 to get 7.68.

$$199-7.68=2x^{2}$$

Subtract 7.68 from 199 to get 191.32.

$$191.32=2x^{2}$$

Swap sides so that all variable terms are on the left hand side.

$$2x^{2}=191.32$$

Subtract 191.32 from both sides.

$$2x^{2}-191.32=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 2 for a, 0 for b, and -191.32 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 2\left(-191.32\right)}}{2\times 2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 2\left(-191.32\right)}}{2\times 2}$$

Multiply -4 times 2.

$$x=\frac{0±\sqrt{-8\left(-191.32\right)}}{2\times 2}$$

Multiply -8 times -191.32.

$$x=\frac{0±\sqrt{1530.56}}{2\times 2}$$

Take the square root of 1530.56.

$$x=\frac{0±\frac{2\sqrt{9566}}{5}}{2\times 2}$$

Multiply 2 times 2.

$$x=\frac{0±\frac{2\sqrt{9566}}{5}}{4}$$

Now solve the equation x=\frac{0±\frac{2\sqrt{9566}}{5}}{4} when ± is plus.

$$x=\frac{\sqrt{9566}}{10}$$

Now solve the equation x=\frac{0±\frac{2\sqrt{9566}}{5}}{4} when ± is minus.

$$x=-\frac{\sqrt{9566}}{10}$$

The equation is now solved.

$$x=\frac{\sqrt{9566}}{10} x=-\frac{\sqrt{9566}}{10}$$