Solve left(a^2-576right)left(a^2-64right)=3465

$$\left( { a }^{ 2 } -576 \right) \left( { a }^{ 2 } -64 \right) = 3465$$

Solve for a

$$a=-\sqrt{320-\sqrt{69001}}\approx -7.570969938$$

$$a=\sqrt{320-\sqrt{69001}}\approx 7.570969938$$

$$a=\sqrt{\sqrt{69001}+320}\approx 24.138774082$$

$$a=-\sqrt{\sqrt{69001}+320}\approx -24.138774082$$

Steps Using the Quadratic Formula

Use the distributive property to multiply a^{2}-576 by a^{2}-64 and combine like terms.

$$a^{4}-640a^{2}+36864=3465$$

Subtract 3465 from both sides.

$$a^{4}-640a^{2}[phone]=0$$

Subtract 3465 from 36864 to get 33399.

$$a^{4}-640a^{2}+33399=0$$

Substitute t for a^{2}.

$$t^{2}-640t+33399=0$$

All equations of the form ax^{2}+bx+c=0 can be solved using the quadratic formula: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. Substitute 1 for a, -640 for b, and 33399 for c in the quadratic formula.

$$t=\frac{-\left(-640\right)±\sqrt{\left(-640\right)^{2}-4\times 1\times 33399}}{2}$$

Do the calculations.

$$t=\frac{640±2\sqrt{69001}}{2}$$

Solve the equation t=\frac{640±2\sqrt{69001}}{2} when ± is plus and when ± is minus.

$$t=\sqrt{69001}+320 t=320-\sqrt{69001}$$

Since a=t^{2}, the solutions are obtained by evaluating a=±\sqrt{t} for each t.

$$a=\sqrt{\sqrt{69001}+320} a=-\sqrt{\sqrt{69001}+320} a=\sqrt{320-\sqrt{69001}} a=-\sqrt{320-\sqrt{69001}}$$