Use the Quadratic Formula to solve 8x^2 − 24x + 18 = 0.

Question
Quadratics
asked 2020-11-23
Use the Quadratic Formula to solve \(\displaystyle{8}{x}^{{2}}−{24}{x}+{18}={0}.\)

Answers (1)

2020-11-24
Simplify this quadratic equation
\(\displaystyle{8}{x}^{{2}}−{24}{x}+{18}={0}\)
\(\displaystyle{4}{x}^{{2}}−{12}{x}+{9}={0}\)
We know that,
The standard quadratic equation is: \(\displaystyle{a}{x}^{{2}}+{b}{x}+{c}={0}\)
Quadratic formula is: \(\displaystyle{x}=\frac{{−{b}\pm\sqrt{{{b}^{{2}}−{4}{a}{c}}}}}{{{2}{a}}}\)
Here, a=4, b=−12, c=9
Let's apply the quadratic formula
\(\displaystyle{x}={\left(-{\left(-{12}\right)}\pm\frac{\sqrt{{{\left(-{12}\right)}^{{2}}-{4}{\left({4}\right)}{\left({9}\right)}}}}{{{2}{\left({4}\right)}}}\right.}\)
\(\displaystyle{x}=\frac{{{12}\pm\sqrt{{{144}-{144}}}}}{{8}}\)
\(\displaystyle{x}=\frac{{12}}{{8}}\)
\(\displaystyle{x}=\frac{{3}}{{2}}\)
0

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