Solve 10^2=8^2*b^2

$${ 10 }^{ 2 } = { 8 }^{ 2 } \times { b }^{ 2 }$$

Solve for b

$$b = \frac{5}{4} = 1\frac{1}{4} = 1.25$$

$$b = -\frac{5}{4} = -1\frac{1}{4} = -1.25$$

Steps Using Difference of Squares

Calculate 10 to the power of 2 and get 100.

$$100=8^{2}b^{2}$$

Calculate 8 to the power of 2 and get 64.

$$100=64b^{2}$$

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

$$64b^{2}=100$$

Subtract 100 from both sides.

$$64b^{2}-100=0$$

Divide both sides by 4.

$$16b^{2}-25=0$$

Consider 16b^{2}-25. Rewrite 16b^{2}-25 as \left(4b\right)^{2}-5^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(4b-5\right)\left(4b+5\right)=0$$

To find equation solutions, solve 4b-5=0 and 4b+5=0.

$$b=\frac{5}{4} b=-\frac{5}{4}$$

Steps by Finding Square Root

Calculate 10 to the power of 2 and get 100.

$$100=8^{2}b^{2}$$

Calculate 8 to the power of 2 and get 64.

$$100=64b^{2}$$

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

$$64b^{2}=100$$

Divide both sides by 64.

$$b^{2}=\frac{100}{64}$$

Reduce the fraction \frac{100}{64} to lowest terms by extracting and canceling out 4.

$$b^{2}=\frac{25}{16}$$

Take the square root of both sides of the equation.

$$b=\frac{5}{4} b=-\frac{5}{4}$$

Steps Using the Quadratic Formula

Calculate 10 to the power of 2 and get 100.

$$100=8^{2}b^{2}$$

Calculate 8 to the power of 2 and get 64.

$$100=64b^{2}$$

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

$$64b^{2}=100$$

Subtract 100 from both sides.

$$64b^{2}-100=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 64 for a, 0 for b, and -100 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$b=\frac{0±\sqrt{0^{2}-4\times 64\left(-100\right)}}{2\times 64}$$

Square 0.

$$b=\frac{0±\sqrt{-4\times 64\left(-100\right)}}{2\times 64}$$

Multiply -4 times 64.

$$b=\frac{0±\sqrt{-256\left(-100\right)}}{2\times 64}$$

Multiply -256 times -100.

$$b=\frac{0±\sqrt{25600}}{2\times 64}$$

Take the square root of 25600.

$$b=\frac{0±160}{2\times 64}$$

Multiply 2 times 64.

$$b=\frac{0±160}{128}$$

Now solve the equation b=\frac{0±160}{128} when ± is plus. Reduce the fraction \frac{160}{128} to lowest terms by extracting and canceling out 32.

$$b=\frac{5}{4}$$

Now solve the equation b=\frac{0±160}{128} when ± is minus. Reduce the fraction \frac{-160}{128} to lowest terms by extracting and canceling out 32.

$$b=-\frac{5}{4}$$

The equation is now solved.

$$b=\frac{5}{4} b=-\frac{5}{4}$$