Question

25p² - 10 p = 2

Quadratic function and equation
ANSWERED
asked 2021-02-25
\(\displaystyle{25}{p}²-{10}{p}={2}\)

Answers (1)

2021-02-26
We are given: \(\displaystyle{25}{p}²-{10}{p}={2}\)
Solve by completing the square. First, we write the equation in the form \(\displaystyle{x}²-{10}{x}={c}\). Divide both sides by 25:
\(\displaystyle{p}²-\frac{{2}}{{5}}{p}=\frac{{2}}{{25}}\)
Complete the square by adding \(\displaystyle{\left(\frac{{b}}{{2}}\right)}^{{2}}\) on both sides. Here, \(\displaystyle{b}=-{\left(\frac{{2}}{{5}}\right)}\) so we add \(\displaystyle{\left(\frac{{-\frac{{2}}{{5}}}}{{2}}\right)}^{{2}}=\frac{{1}}{{25}}\) to both sides:
\(\displaystyle{p}²-\frac{{2}}{{5}}{p}+\frac{{1}}{{25}}=\frac{{2}}{{25}}+\frac{{1}}{{25}}\)
\(\displaystyle{\left({p}-{\left(\frac{{1}}{{5}}\right)}\right)}^{{2}}=\frac{{3}}{{25}}\)
Take the square root of both sides: \(\displaystyle{p}-{\left(\frac{{1}}{{5}}\right)}=\pm\frac{\sqrt{{3}}}{{5}}\)
Add 1/5 to both sides: \(\displaystyle{p}=\frac{{1}}{{5}}\pm\frac{\sqrt{{3}}}{{5}}\)
\(\displaystyle{p}=\frac{{{1}\pm\sqrt{{3}}}}{{5}}\)
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