Solve 1/2*30*(253^2-x^2)=-30*155

$$\frac{ 1 }{ 2 } \times 30 \times ( { 253 }^{ 2 } - { x }^{ 2 } )=-30 \times 155$$

Solve for x

$$x=\sqrt{64319}\approx 253.611908238$$

$$x=-\sqrt{64319}\approx -253.611908238$$

Steps by Finding Square Root

Multiply \frac{1}{2} and 30 to get 15.

$$15\left(253^{2}-x^{2}\right)=-30\times 155$$

Calculate 253 to the power of 2 and get 64009.

$$15\left(64009-x^{2}\right)=-30\times 155$$

Use the distributive property to multiply 15 by 64009-x^{2}.

$$960135-15x^{2}=-30\times 155$$

Multiply -30 and 155 to get -4650.

$$960135-15x^{2}=-4650$$

Subtract 960135 from both sides.

$$-15x^{2}=-4650-960135$$

Subtract 960135 from -4650 to get -964785.

$$-15x^{2}=-964785$$

Divide both sides by -15.

$$x^{2}=\frac{-964785}{-15}$$

Divide -964785 by -15 to get 64319.

$$x^{2}=64319$$

Take the square root of both sides of the equation.

$$x=\sqrt{64319} x=-\sqrt{64319}$$

Steps Using the Quadratic Formula

Multiply \frac{1}{2} and 30 to get 15.

$$15\left(253^{2}-x^{2}\right)=-30\times 155$$

Calculate 253 to the power of 2 and get 64009.

$$15\left(64009-x^{2}\right)=-30\times 155$$

Use the distributive property to multiply 15 by 64009-x^{2}.

$$960135-15x^{2}=-30\times 155$$

Multiply -30 and 155 to get -4650.

$$960135-15x^{2}=-4650$$

Add 4650 to both sides.

$$960135-15x^{2}+4650=0$$

Add 960135 and 4650 to get 964785.

$$964785-15x^{2}=0$$

Quadratic equations like this one, with an x^{2} term but no x term, can still be solved using the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}, once they are put in standard form: ax^{2}+bx+c=0.

$$-15x^{2}+964785=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -15 for a, 0 for b, and 964785 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-15\right)\times 964785}}{2\left(-15\right)}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-15\right)\times 964785}}{2\left(-15\right)}$$

Multiply -4 times -15.

$$x=\frac{0±\sqrt{60\times 964785}}{2\left(-15\right)}$$

Multiply 60 times 964785.

$$x=\frac{0±\sqrt{57887100}}{2\left(-15\right)}$$

Take the square root of 57887100.

$$x=\frac{0±30\sqrt{64319}}{2\left(-15\right)}$$

Multiply 2 times -15.

$$x=\frac{0±30\sqrt{64319}}{-30}$$

Now solve the equation x=\frac{0±30\sqrt{64319}}{-30} when ± is plus.

$$x=-\sqrt{64319}$$

Now solve the equation x=\frac{0±30\sqrt{64319}}{-30} when ± is minus.

$$x=\sqrt{64319}$$

The equation is now solved.

$$x=-\sqrt{64319} x=\sqrt{64319}$$