Solve 5^2*z^2=7^2

$${ 5 }^{ 2 } \times { z }^{ 2 } = { 7 }^{ 2 }$$

Solve for z

$$z = \frac{7}{5} = 1\frac{2}{5} = 1.4$$

$$z = -\frac{7}{5} = -1\frac{2}{5} = -1.4$$

Steps Using Difference of Squares

Calculate 5 to the power of 2 and get 25.

$$25z^{2}=7^{2}$$

Calculate 7 to the power of 2 and get 49.

$$25z^{2}=49$$

Subtract 49 from both sides.

$$25z^{2}-49=0$$

Consider 25z^{2}-49. Rewrite 25z^{2}-49 as \left(5z\right)^{2}-7^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(5z-7\right)\left(5z+7\right)=0$$

To find equation solutions, solve 5z-7=0 and 5z+7=0.

$$z=\frac{7}{5} z=-\frac{7}{5}$$

Steps by Finding Square Root

Calculate 5 to the power of 2 and get 25.

$$25z^{2}=7^{2}$$

Calculate 7 to the power of 2 and get 49.

$$25z^{2}=49$$

Divide both sides by 25.

$$z^{2}=\frac{49}{25}$$

Take the square root of both sides of the equation.

$$z=\frac{7}{5} z=-\frac{7}{5}$$

Steps Using the Quadratic Formula

Calculate 5 to the power of 2 and get 25.

$$25z^{2}=7^{2}$$

Calculate 7 to the power of 2 and get 49.

$$25z^{2}=49$$

Subtract 49 from both sides.

$$25z^{2}-49=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 25 for a, 0 for b, and -49 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$z=\frac{0±\sqrt{0^{2}-4\times 25\left(-49\right)}}{2\times 25}$$

Square 0.

$$z=\frac{0±\sqrt{-4\times 25\left(-49\right)}}{2\times 25}$$

Multiply -4 times 25.

$$z=\frac{0±\sqrt{-100\left(-49\right)}}{2\times 25}$$

Multiply -100 times -49.

$$z=\frac{0±\sqrt{4900}}{2\times 25}$$

Take the square root of 4900.

$$z=\frac{0±70}{2\times 25}$$

Multiply 2 times 25.

$$z=\frac{0±70}{50}$$

Now solve the equation z=\frac{0±70}{50} when ± is plus. Reduce the fraction \frac{70}{50} to lowest terms by extracting and canceling out 10.

$$z=\frac{7}{5}$$

Now solve the equation z=\frac{0±70}{50} when ± is minus. Reduce the fraction \frac{-70}{50} to lowest terms by extracting and canceling out 10.

$$z=-\frac{7}{5}$$

The equation is now solved.

$$z=\frac{7}{5} z=-\frac{7}{5}$$