Solve 18^2/25-a^2+29*19/5=0

$$\frac { 18 ^ { 2 } } { 25 } - a ^ { 2 } + \frac { 29 \times 19 } { 5 } = 0$$

Solve for a

$$a = \frac{\sqrt{3079}}{5} \approx 11.097747519$$

$$a = -\frac{\sqrt{3079}}{5} \approx -11.097747519$$

Steps by Finding Square Root

Multiply both sides of the equation by 25, the least common multiple of 25,5.

$$18^{2}-25a^{2}+5\times 29\times 19=0$$

Calculate 18 to the power of 2 and get 324.

$$324-25a^{2}+5\times 29\times 19=0$$

Multiply 5 and 29 to get 145.

$$324-25a^{2}+145\times 19=0$$

Multiply 145 and 19 to get 2755.

$$324-25a^{2}+2755=0$$

Add 324 and 2755 to get 3079.

$$3079-25a^{2}=0$$

Subtract 3079 from both sides. Anything subtracted from zero gives its negation.

$$-25a^{2}=-3079$$

Divide both sides by -25.

$$a^{2}=\frac{-3079}{-25}$$

Fraction \frac{-3079}{-25} can be simplified to \frac{3079}{25} by removing the negative sign from both the numerator and the denominator.

$$a^{2}=\frac{3079}{25}$$

Take the square root of both sides of the equation.

$$a=\frac{\sqrt{3079}}{5} a=-\frac{\sqrt{3079}}{5}$$

Steps Using the Quadratic Formula

Multiply both sides of the equation by 25, the least common multiple of 25,5.

$$18^{2}-25a^{2}+5\times 29\times 19=0$$

Calculate 18 to the power of 2 and get 324.

$$324-25a^{2}+5\times 29\times 19=0$$

Multiply 5 and 29 to get 145.

$$324-25a^{2}+145\times 19=0$$

Multiply 145 and 19 to get 2755.

$$324-25a^{2}+2755=0$$

Add 324 and 2755 to get 3079.

$$3079-25a^{2}=0$$

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.

$$-25a^{2}+3079=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -25 for a, 0 for b, and 3079 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$a=\frac{0±\sqrt{0^{2}-4\left(-25\right)\times 3079}}{2\left(-25\right)}$$

Square 0.

$$a=\frac{0±\sqrt{-4\left(-25\right)\times 3079}}{2\left(-25\right)}$$

Multiply -4 times -25.

$$a=\frac{0±\sqrt{100\times 3079}}{2\left(-25\right)}$$

Multiply 100 times 3079.

$$a=\frac{0±\sqrt{307900}}{2\left(-25\right)}$$

Take the square root of 307900.

$$a=\frac{0±10\sqrt{3079}}{2\left(-25\right)}$$

Multiply 2 times -25.

$$a=\frac{0±10\sqrt{3079}}{-50}$$

Now solve the equation a=\frac{0±10\sqrt{3079}}{-50} when ± is plus.

$$a=-\frac{\sqrt{3079}}{5}$$

Now solve the equation a=\frac{0±10\sqrt{3079}}{-50} when ± is minus.

$$a=\frac{\sqrt{3079}}{5}$$

The equation is now solved.

$$a=-\frac{\sqrt{3079}}{5} a=\frac{\sqrt{3079}}{5}$$