How do You Solve for “x” in a Quadratic Equation?
Algebra Math Problem: Find the value of x from the quadratic equation 8x3/2n − 8x−3/2n = 63
Solution
Multiply by x3/2n and transpose; thus
8 x3/2n − 8 x−3/2n = 8 x9/4n² − 8 = 63 x3/2n
⇒ 8 x9/4n² − 63 x3/2n − 8 = 0
Let x3/2n = t , then
8 x9/4n² − 63 x3/2n − 8 = 8 x(3/2n)² − 63 x3/2n − 8 = 0
⇒ 8 x(3/2n)² − 63 x3/2n = 8t² − 63t − 8 = 0
8t² − 63t − 8 is a quartratic equation so
\begin{aligned}
t&=\dfrac{63 \pm \sqrt{63^2-4\times 8 \times(-8)}}{2 \times 8} \\
\\
&=\dfrac{63 \pm \sqrt{3969+256}}{16} \\
\\
&=\dfrac{63 \pm \sqrt{4225}}{16} \\
\\
&=\dfrac{63 \pm 65}{16} \\
\\
\Rightarrow t&=8 , \ \dfrac{1}{8}\\
\end{aligned}When t = 8
x3/2n = 8
⇒ x = 82n/3
⇒ x = 4n
When t = 1/8
x3/2n = 1/8
⇒ x = 8−2n/3
⇒ x = 4−n
Thus, solution to this quadratic equation is x = 4n and x = 4−n
