Solve 25^2=x^2*7^2

$$25 ^ { 2 } = x ^ { 2 } \times 7 ^ { 2 }$$

Solve for x

$$x = \frac{25}{7} = 3\frac{4}{7} \approx 3.571428571$$

$$x = -\frac{25}{7} = -3\frac{4}{7} \approx -3.571428571$$

Steps Using Difference of Squares

Calculate 25 to the power of 2 and get 625.

$$625=x^{2}\times 7^{2}$$

Calculate 7 to the power of 2 and get 49.

$$625=x^{2}\times 49$$

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

$$x^{2}\times 49=625$$

Subtract 625 from both sides.

$$x^{2}\times 49-625=0$$

Consider x^{2}\times 49-625. Rewrite x^{2}\times 49-625 as \left(7x\right)^{2}-25^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(7x-25\right)\left(7x+25\right)=0$$

To find equation solutions, solve 7x-25=0 and 7x+25=0.

$$x=\frac{25}{7} x=-\frac{25}{7}$$

Steps by Finding Square Root

Calculate 25 to the power of 2 and get 625.

$$625=x^{2}\times 7^{2}$$

Calculate 7 to the power of 2 and get 49.

$$625=x^{2}\times 49$$

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

$$x^{2}\times 49=625$$

Divide both sides by 49.

$$x^{2}=\frac{625}{49}$$

Take the square root of both sides of the equation.

$$x=\frac{25}{7} x=-\frac{25}{7}$$

Steps Using the Quadratic Formula

Calculate 25 to the power of 2 and get 625.

$$625=x^{2}\times 7^{2}$$

Calculate 7 to the power of 2 and get 49.

$$625=x^{2}\times 49$$

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

$$x^{2}\times 49=625$$

Subtract 625 from both sides.

$$x^{2}\times 49-625=0$$

Quadratic equations like this one, with an x^{2} term but no x term, can still be solved using the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}, once they are put in standard form: ax^{2}+bx+c=0.

$$49x^{2}-625=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 49 for a, 0 for b, and -625 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 49\left(-625\right)}}{2\times 49}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 49\left(-625\right)}}{2\times 49}$$

Multiply -4 times 49.

$$x=\frac{0±\sqrt{-196\left(-625\right)}}{2\times 49}$$

Multiply -196 times -625.

$$x=\frac{0±\sqrt{122500}}{2\times 49}$$

Take the square root of 122500.

$$x=\frac{0±350}{2\times 49}$$

Multiply 2 times 49.

$$x=\frac{0±350}{98}$$

Now solve the equation x=\frac{0±350}{98} when ± is plus. Reduce the fraction \frac{350}{98} to lowest terms by extracting and canceling out 14.

$$x=\frac{25}{7}$$

Now solve the equation x=\frac{0±350}{98} when ± is minus. Reduce the fraction \frac{-350}{98} to lowest terms by extracting and canceling out 14.

$$x=-\frac{25}{7}$$

The equation is now solved.

$$x=\frac{25}{7} x=-\frac{25}{7}$$