# How do you solve the quadratic 8b^2-1=-78 using any method?

Jan 2, 2017

$b = \frac{i \sqrt{77} \sqrt{2}}{4} = \frac{i \sqrt{154}}{4} \approx i 3.1024 \ldots$

#### Explanation:

$8 {b}^{2} = - 77$

Divide both sides by 8

${b}^{2} = - \frac{77}{8} - 9.625 \leftarrow \text{ as a check value}$

$b = \frac{\sqrt{- 77}}{\sqrt{2 \times {2}^{2}}}$

$b = \frac{i \sqrt{77}}{2 \sqrt{2}} \times 1 = \frac{i \sqrt{77}}{2 \sqrt{2}} \times \frac{\sqrt{2}}{\sqrt{2}}$

$b = \frac{i \sqrt{77} \sqrt{2}}{4} = \frac{i \sqrt{154}}{4} \approx i 3.1024 \ldots$
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Check

${b}^{2} = {\left(\frac{i \sqrt{154}}{4}\right)}^{2}$

${b}^{2} = - \frac{154}{16}$

${b}^{2} = - 9.625 \leftarrow \text{ check confirmed}$