Solve 1/2x^2=100*0.6+0.25*100*08

$$\frac { 1 } { 2 } x ^ { 2 } = 100 \times 0.6 + 0.25 \times 100 \times 08$$

Solve for x

$$x=2\sqrt{30}\approx 10.95445115$$

$$x=-2\sqrt{30}\approx -10.95445115$$

Steps by Finding Square Root

Multiply 100 and 0.6 to get 60.

$$\frac{1}{2}x^{2}=60+0.25\times 100\times 0\times 8$$

Multiply 0.25 and 100 to get 25.

$$\frac{1}{2}x^{2}=60+25\times 0\times 8$$

Multiply 25 and 0 to get 0.

$$\frac{1}{2}x^{2}=60+0\times 8$$

Multiply 0 and 8 to get 0.

$$\frac{1}{2}x^{2}=60+0$$

Add 60 and 0 to get 60.

$$\frac{1}{2}x^{2}=60$$

Multiply both sides by 2, the reciprocal of \frac{1}{2}.

$$x^{2}=60\times 2$$

Multiply 60 and 2 to get 120.

$$x^{2}=120$$

Take the square root of both sides of the equation.

$$x=2\sqrt{30} x=-2\sqrt{30}$$

Steps Using the Quadratic Formula

Multiply 100 and 0.6 to get 60.

$$\frac{1}{2}x^{2}=60+0.25\times 100\times 0\times 8$$

Multiply 0.25 and 100 to get 25.

$$\frac{1}{2}x^{2}=60+25\times 0\times 8$$

Multiply 25 and 0 to get 0.

$$\frac{1}{2}x^{2}=60+0\times 8$$

Multiply 0 and 8 to get 0.

$$\frac{1}{2}x^{2}=60+0$$

Add 60 and 0 to get 60.

$$\frac{1}{2}x^{2}=60$$

Subtract 60 from both sides.

$$\frac{1}{2}x^{2}-60=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute \frac{1}{2} for a, 0 for b, and -60 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times \frac{1}{2}\left(-60\right)}}{2\times \frac{1}{2}}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times \frac{1}{2}\left(-60\right)}}{2\times \frac{1}{2}}$$

Multiply -4 times \frac{1}{2}.

$$x=\frac{0±\sqrt{-2\left(-60\right)}}{2\times \frac{1}{2}}$$

Multiply -2 times -60.

$$x=\frac{0±\sqrt{120}}{2\times \frac{1}{2}}$$

Take the square root of 120.

$$x=\frac{0±2\sqrt{30}}{2\times \frac{1}{2}}$$

Multiply 2 times \frac{1}{2}.

$$x=\frac{0±2\sqrt{30}}{1}$$

Now solve the equation x=\frac{0±2\sqrt{30}}{1} when ± is plus.

$$x=2\sqrt{30}$$

Now solve the equation x=\frac{0±2\sqrt{30}}{1} when ± is minus.

$$x=-2\sqrt{30}$$

The equation is now solved.

$$x=2\sqrt{30} x=-2\sqrt{30}$$