Solve a^4-64a^2+25*36=0

$$a ^ { 4 } - 64 a ^ { 2 } + 25 \times 36 = 0$$

Solve for a (complex solution)

$$a=\sqrt{31}-1\approx 4.567764363$$

$$a=1-\sqrt{31}\approx -4.567764363$$

$$a=-\left(\sqrt{31}+1\right)\approx -6.567764363$$

$$a=\sqrt{31}+1\approx 6.567764363$$

Steps Using the Quadratic Formula

Multiply 25 and 36 to get 900.

$$a^{4}-64a^{2}+900=0$$

Substitute t for a^{2}.

$$t^{2}-64t+900=0$$

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, -64 for b, and 900 for c in the quadratic formula.

$$t=\frac{-\left(-64\right)±\sqrt{\left(-64\right)^{2}-4\times 1\times 900}}{2}$$

Do the calculations.

$$t=\frac{64±4\sqrt{31}}{2}$$

Solve the equation t=\frac{64±4\sqrt{31}}{2} when ± is plus and when ± is minus.

$$t=2\sqrt{31}+32 t=32-2\sqrt{31}$$

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

$$a=-\left(\sqrt{31}+1\right) a=\sqrt{31}+1 a=1-\sqrt{31} a=-\left(1-\sqrt{31}\right)$$

Solve for a

$$a=1-\sqrt{31}\approx -4.567764363$$

$$a=\sqrt{31}-1\approx 4.567764363$$

$$a=\sqrt{31}+1\approx 6.567764363$$

$$a=-\sqrt{31}-1\approx -6.567764363$$

Steps Using the Quadratic Formula

Multiply 25 and 36 to get 900.

$$a^{4}-64a^{2}+900=0$$

Substitute t for a^{2}.

$$t^{2}-64t+900=0$$

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, -64 for b, and 900 for c in the quadratic formula.

$$t=\frac{-\left(-64\right)±\sqrt{\left(-64\right)^{2}-4\times 1\times 900}}{2}$$

Do the calculations.

$$t=\frac{64±4\sqrt{31}}{2}$$

Solve the equation t=\frac{64±4\sqrt{31}}{2} when ± is plus and when ± is minus.

$$t=2\sqrt{31}+32 t=32-2\sqrt{31}$$

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

$$a=\sqrt{31}+1 a=-\left(\sqrt{31}+1\right) a=-\left(1-\sqrt{31}\right) a=1-\sqrt{31}$$