Solve 34^2*84^2=x^2

$$34 ^ { 2 } \times 84 ^ { 2 } = x ^ { 2 }$$

Solve for x

$$x=2856$$

$$x=-2856$$

Steps Using Difference of Squares

Calculate 34 to the power of 2 and get 1156.

$$1156\times 84^{2}=x^{2}$$

Calculate 84 to the power of 2 and get 7056.

$$1156\times 7056=x^{2}$$

Multiply 1156 and 7056 to get 8156736.

$$8156736=x^{2}$$

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

$$x^{2}=8156736$$

Subtract 8156736 from both sides.

$$x^{2}-8156736=0$$

Consider x^{2}-8156736. Rewrite x^{2}-8156736 as x^{2}-2856^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(x-2856\right)\left(x+2856\right)=0$$

To find equation solutions, solve x-2856=0 and x+2856=0.

$$x=2856 x=-2856$$

Steps by Finding Square Root

Calculate 34 to the power of 2 and get 1156.

$$1156\times 84^{2}=x^{2}$$

Calculate 84 to the power of 2 and get 7056.

$$1156\times 7056=x^{2}$$

Multiply 1156 and 7056 to get 8156736.

$$8156736=x^{2}$$

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

$$x^{2}=8156736$$

Take the square root of both sides of the equation.

$$x=2856 x=-2856$$

Steps Using the Quadratic Formula

Calculate 34 to the power of 2 and get 1156.

$$1156\times 84^{2}=x^{2}$$

Calculate 84 to the power of 2 and get 7056.

$$1156\times 7056=x^{2}$$

Multiply 1156 and 7056 to get 8156736.

$$8156736=x^{2}$$

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

$$x^{2}=8156736$$

Subtract 8156736 from both sides.

$$x^{2}-8156736=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -8156736 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-8156736\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-8156736\right)}}{2}$$

Multiply -4 times -8156736.

$$x=\frac{0±\sqrt{32626944}}{2}$$

Take the square root of 32626944.

$$x=\frac{0±5712}{2}$$

Now solve the equation x=\frac{0±5712}{2} when ± is plus. Divide 5712 by 2.

$$x=2856$$

Now solve the equation x=\frac{0±5712}{2} when ± is minus. Divide -5712 by 2.

$$x=-2856$$

The equation is now solved.

$$x=2856 x=-2856$$