Solve 648^2=a^2-704*648-352^2

$$648 ^ { 2 } = a ^ { 2 } - 704 \times 648 - 352 ^ { 2 }$$

Solve for a

$$a=1000$$

$$a=-1000$$

Steps Using Difference of Squares

Calculate 648 to the power of 2 and get 419904.

$$419904=a^{2}-704\times 648-352^{2}$$

Multiply 704 and 648 to get 456192.

$$419904=a^{2}-456192-352^{2}$$

Calculate 352 to the power of 2 and get 123904.

$$419904=a^{2}-456192-123904$$

Subtract 123904 from -456192 to get -580096.

$$419904=a^{2}-580096$$

Swap sides so that all variable terms are on the left hand side.

$$a^{2}-580096=419904$$

Subtract 419904 from both sides.

$$a^{2}-580096-419904=0$$

Subtract 419904 from -580096 to get -1000000.

$$a^{2}-1000000=0$$

Consider a^{2}-1000000. Rewrite a^{2}-1000000 as a^{2}-1000^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(a-1000\right)\left(a+1000\right)=0$$

To find equation solutions, solve a-1000=0 and a+1000=0.

$$a=1000 a=-1000$$

Steps by Finding Square Root

Calculate 648 to the power of 2 and get 419904.

$$419904=a^{2}-704\times 648-352^{2}$$

Multiply 704 and 648 to get 456192.

$$419904=a^{2}-456192-352^{2}$$

Calculate 352 to the power of 2 and get 123904.

$$419904=a^{2}-456192-123904$$

Subtract 123904 from -456192 to get -580096.

$$419904=a^{2}-580096$$

Swap sides so that all variable terms are on the left hand side.

$$a^{2}-580096=419904$$

Add 580096 to both sides.

$$a^{2}=419904+580096$$

Add 419904 and 580096 to get 1000000.

$$a^{2}=1000000$$

Take the square root of both sides of the equation.

$$a=1000 a=-1000$$

Steps Using the Quadratic Formula

Calculate 648 to the power of 2 and get 419904.

$$419904=a^{2}-704\times 648-352^{2}$$

Multiply 704 and 648 to get 456192.

$$419904=a^{2}-456192-352^{2}$$

Calculate 352 to the power of 2 and get 123904.

$$419904=a^{2}-456192-123904$$

Subtract 123904 from -456192 to get -580096.

$$419904=a^{2}-580096$$

Swap sides so that all variable terms are on the left hand side.

$$a^{2}-580096=419904$$

Subtract 419904 from both sides.

$$a^{2}-580096-419904=0$$

Subtract 419904 from -580096 to get -1000000.

$$a^{2}-1000000=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -1000000 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$a=\frac{0±\sqrt{0^{2}-4\left(-1000000\right)}}{2}$$

Square 0.

$$a=\frac{0±\sqrt{-4\left(-1000000\right)}}{2}$$

Multiply -4 times -1000000.

$$a=\frac{0±\sqrt{4000000}}{2}$$

Take the square root of 4000000.

$$a=\frac{0±2000}{2}$$

Now solve the equation a=\frac{0±2000}{2} when ± is plus. Divide 2000 by 2.

$$a=1000$$

Now solve the equation a=\frac{0±2000}{2} when ± is minus. Divide -2000 by 2.

$$a=-1000$$

The equation is now solved.

$$a=1000 a=-1000$$