Solve 32^2=(x*9)*(x*9)+left(x*21right)*left(x*21right)

$${ 32 }^{ 2 } = (x \times 9) \times (x \times 9)+ \left( x \times 21 \right) \times \left( x \times 21 \right)$$

Solve for x

$$x = \frac{16 \sqrt{58}}{87} \approx 1.400601951$$

$$x = -\frac{16 \sqrt{58}}{87} \approx -1.400601951$$

Steps by Finding Square Root

Multiply x and x to get x^{2}.

$$32^{2}=x^{2}\times 9\times 9+x\times 21x\times 21$$

Multiply x and x to get x^{2}.

$$32^{2}=x^{2}\times 9\times 9+x^{2}\times 21\times 21$$

Calculate 32 to the power of 2 and get 1024.

$$1024=x^{2}\times 9\times 9+x^{2}\times 21\times 21$$

Multiply 9 and 9 to get 81.

$$1024=x^{2}\times 81+x^{2}\times 21\times 21$$

Multiply 21 and 21 to get 441.

$$1024=x^{2}\times 81+x^{2}\times 441$$

Combine x^{2}\times 81 and x^{2}\times 441 to get 522x^{2}.

$$1024=522x^{2}$$

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

$$522x^{2}=1024$$

Divide both sides by 522.

$$x^{2}=\frac{1024}{522}$$

Reduce the fraction \frac{1024}{522} to lowest terms by extracting and canceling out 2.

$$x^{2}=\frac{512}{261}$$

Take the square root of both sides of the equation.

$$x=\frac{16\sqrt{58}}{87} x=-\frac{16\sqrt{58}}{87}$$

Steps Using the Quadratic Formula

Multiply x and x to get x^{2}.

$$32^{2}=x^{2}\times 9\times 9+x\times 21x\times 21$$

Multiply x and x to get x^{2}.

$$32^{2}=x^{2}\times 9\times 9+x^{2}\times 21\times 21$$

Calculate 32 to the power of 2 and get 1024.

$$1024=x^{2}\times 9\times 9+x^{2}\times 21\times 21$$

Multiply 9 and 9 to get 81.

$$1024=x^{2}\times 81+x^{2}\times 21\times 21$$

Multiply 21 and 21 to get 441.

$$1024=x^{2}\times 81+x^{2}\times 441$$

Combine x^{2}\times 81 and x^{2}\times 441 to get 522x^{2}.

$$1024=522x^{2}$$

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

$$522x^{2}=1024$$

Subtract 1024 from both sides.

$$522x^{2}-1024=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 522 for a, 0 for b, and -1024 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 522\left(-1024\right)}}{2\times 522}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 522\left(-1024\right)}}{2\times 522}$$

Multiply -4 times 522.

$$x=\frac{0±\sqrt{-2088\left(-1024\right)}}{2\times 522}$$

Multiply -2088 times -1024.

$$x=\frac{0±\sqrt{2138112}}{2\times 522}$$

Take the square root of 2138112.

$$x=\frac{0±192\sqrt{58}}{2\times 522}$$

Multiply 2 times 522.

$$x=\frac{0±192\sqrt{58}}{1044}$$

Now solve the equation x=\frac{0±192\sqrt{58}}{1044} when ± is plus.

$$x=\frac{16\sqrt{58}}{87}$$

Now solve the equation x=\frac{0±192\sqrt{58}}{1044} when ± is minus.

$$x=-\frac{16\sqrt{58}}{87}$$

The equation is now solved.

$$x=\frac{16\sqrt{58}}{87} x=-\frac{16\sqrt{58}}{87}$$