Solve y^2=52-48*(-0,8)

$$y ^ { 2 } = 52 - 48 \cdot ( - 0,8 )$$

Solve for y

$$y = \frac{2 \sqrt{565}}{5} \approx 9.507891459$$

$$y = -\frac{2 \sqrt{565}}{5} \approx -9.507891459$$

Steps by Finding Square Root

Multiply 48 and -0,8 to get -38,4.

$$y^{2}=52-\left(-38,4\right)$$

The opposite of -38,4 is 38,4.

$$y^{2}=52+38,4$$

Add 52 and 38,4 to get 90,4.

$$y^{2}=90,4$$

Take the square root of both sides of the equation.

$$y=\frac{2\sqrt{565}}{5} y=-\frac{2\sqrt{565}}{5}$$

Steps Using the Quadratic Formula

Multiply 48 and -0,8 to get -38,4.

$$y^{2}=52-\left(-38,4\right)$$

The opposite of -38,4 is 38,4.

$$y^{2}=52+38,4$$

Add 52 and 38,4 to get 90,4.

$$y^{2}=90,4$$

Subtract 90,4 from both sides.

$$y^{2}-90,4=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -90,4 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$y=\frac{0±\sqrt{0^{2}-4\left(-90,4\right)}}{2}$$

Square 0.

$$y=\frac{0±\sqrt{-4\left(-90,4\right)}}{2}$$

Multiply -4 times -90,4.

$$y=\frac{0±\sqrt{361,6}}{2}$$

Take the square root of 361,6.

$$y=\frac{0±\frac{4\sqrt{565}}{5}}{2}$$

Now solve the equation y=\frac{0±\frac{4\sqrt{565}}{5}}{2} when ± is plus.

$$y=\frac{2\sqrt{565}}{5}$$

Now solve the equation y=\frac{0±\frac{4\sqrt{565}}{5}}{2} when ± is minus.

$$y=-\frac{2\sqrt{565}}{5}$$

The equation is now solved.

$$y=\frac{2\sqrt{565}}{5} y=-\frac{2\sqrt{565}}{5}$$