How do you solve 8b^2-7=193?

Sep 4, 2016

$b = \pm 5$

Explanation:

$8 {b}^{2} - 7 = 193$

or

$8 {b}^{2} = 193 + 7$

or

$8 {b}^{2} = 200$

or

${b}^{2} = \frac{200}{8}$

or

${b}^{2} = 25$

or

$b = \sqrt{25}$

or

$b = \pm 5$

Sep 4, 2016

$x = \pm 5$

Explanation:

Usually a quadratic equation is solved by making it equal to 0.
However this is a special case where there is no term in $x$.

Isolate the ${x}^{2}$ term by adding 7 to both sides.

$8 {x}^{2} - 7 \textcolor{b l u e}{+ 7} = 193 \textcolor{b l u e}{+ 7}$

$8 {x}^{2} = 200 \text{ } \leftarrow \div 8$

${x}^{2} = 25$

$x = \pm \sqrt{25}$

$x = \pm 5$