Solve 1/2*30*(25.3^2-x^2)=-30*15.5

$$\frac{ 1 }{ 2 } \times 30 \times ( { 25.3 }^{ 2 } - { x }^{ 2 } )=-30 \times 15.5$$

Solve for x

$$x = \frac{\sqrt{67109}}{10} \approx 25.905404841$$

$$x = -\frac{\sqrt{67109}}{10} \approx -25.905404841$$

Steps by Finding Square Root

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

$$15\left(25.3^{2}-x^{2}\right)=-30\times 15.5$$

Calculate 25.3 to the power of 2 and get 640.09.

$$15\left(640.09-x^{2}\right)=-30\times 15.5$$

Use the distributive property to multiply 15 by 640.09-x^{2}.

$$9601.35-15x^{2}=-30\times 15.5$$

Multiply -30 and 15.5 to get -465.

$$9601.35-15x^{2}=-465$$

Subtract 9601.35 from both sides.

$$-15x^{2}=-465-9601.35$$

Subtract 9601.35 from -465 to get -10066.35.

$$-15x^{2}=-10066.35$$

Divide both sides by -15.

$$x^{2}=\frac{-10066.35}{-15}$$

Expand \frac{-10066.35}{-15} by multiplying both numerator and the denominator by 100.

$$x^{2}=\frac{-1006635}{-1500}$$

Reduce the fraction \frac{-1006635}{-1500} to lowest terms by extracting and canceling out -15.

$$x^{2}=\frac{67109}{100}$$

Take the square root of both sides of the equation.

$$x=\frac{\sqrt{67109}}{10} x=-\frac{\sqrt{67109}}{10}$$

Steps Using the Quadratic Formula

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

$$15\left(25.3^{2}-x^{2}\right)=-30\times 15.5$$

Calculate 25.3 to the power of 2 and get 640.09.

$$15\left(640.09-x^{2}\right)=-30\times 15.5$$

Use the distributive property to multiply 15 by 640.09-x^{2}.

$$9601.35-15x^{2}=-30\times 15.5$$

Multiply -30 and 15.5 to get -465.

$$9601.35-15x^{2}=-465$$

Add 465 to both sides.

$$9601.35-15x^{2}+465=0$$

Add 9601.35 and 465 to get 10066.35.

$$10066.35-15x^{2}=0$$

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.

$$-15x^{2}+10066.35=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -15 for a, 0 for b, and 10066.35 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-15\right)\times 10066.35}}{2\left(-15\right)}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-15\right)\times 10066.35}}{2\left(-15\right)}$$

Multiply -4 times -15.

$$x=\frac{0±\sqrt{60\times 10066.35}}{2\left(-15\right)}$$

Multiply 60 times 10066.35.

$$x=\frac{0±\sqrt{603981}}{2\left(-15\right)}$$

Take the square root of 603981.

$$x=\frac{0±3\sqrt{67109}}{2\left(-15\right)}$$

Multiply 2 times -15.

$$x=\frac{0±3\sqrt{67109}}{-30}$$

Now solve the equation x=\frac{0±3\sqrt{67109}}{-30} when ± is plus.

$$x=-\frac{\sqrt{67109}}{10}$$

Now solve the equation x=\frac{0±3\sqrt{67109}}{-30} when ± is minus.

$$x=\frac{\sqrt{67109}}{10}$$

The equation is now solved.

$$x=-\frac{\sqrt{67109}}{10} x=\frac{\sqrt{67109}}{10}$$