Solve 1.9=0.05*x^2/0.5

$$1.9 = 0.05 \times \frac { x ^ { 2 } } { 0.5 }$$

Solve for x

$$x=\sqrt{19}\approx 4.358898944$$

$$x=-\sqrt{19}\approx -4.358898944$$

Steps by Finding Square Root

Divide both sides by 0.05.

$$\frac{1.9}{0.05}=\frac{x^{2}}{0.5}$$

Expand \frac{1.9}{0.05} by multiplying both numerator and the denominator by 100.

$$\frac{190}{5}=\frac{x^{2}}{0.5}$$

Divide 190 by 5 to get 38.

$$38=\frac{x^{2}}{0.5}$$

Multiply both sides by 0.5.

$$38\times 0.5=x^{2}$$

Multiply 38 and 0.5 to get 19.

$$19=x^{2}$$

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

$$x^{2}=19$$

Take the square root of both sides of the equation.

$$x=\sqrt{19} x=-\sqrt{19}$$

Steps Using the Quadratic Formula

Divide both sides by 0.05.

$$\frac{1.9}{0.05}=\frac{x^{2}}{0.5}$$

Expand \frac{1.9}{0.05} by multiplying both numerator and the denominator by 100.

$$\frac{190}{5}=\frac{x^{2}}{0.5}$$

Divide 190 by 5 to get 38.

$$38=\frac{x^{2}}{0.5}$$

Multiply both sides by 0.5.

$$38\times 0.5=x^{2}$$

Multiply 38 and 0.5 to get 19.

$$19=x^{2}$$

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

$$x^{2}=19$$

Subtract 19 from both sides.

$$x^{2}-19=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -19 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-19\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-19\right)}}{2}$$

Multiply -4 times -19.

$$x=\frac{0±\sqrt{76}}{2}$$

Take the square root of 76.

$$x=\frac{0±2\sqrt{19}}{2}$$

Now solve the equation x=\frac{0±2\sqrt{19}}{2} when ± is plus.

$$x=\sqrt{19}$$

Now solve the equation x=\frac{0±2\sqrt{19}}{2} when ± is minus.

$$x=-\sqrt{19}$$

The equation is now solved.

$$x=\sqrt{19} x=-\sqrt{19}$$