Question
$$(1+r)^2 = \frac{905}{1000}$$
Answer
$$ \begin{matrix}r_1 = -1-\dfrac{\sqrt{ 362 }}{ 20 } & r_2 = -1+\dfrac{\sqrt{ 362 }}{ 20 } \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} (1+r)^2 &= \frac{905}{1000}&& \text{multiply ALL terms by } \color{blue}{ 1000 }. \\[1 em]1000(1+r)^2 &= 1000\cdot\frac{905}{1000}&& \text{cancel out the denominators} \\[1 em]1000(1+r)^2 &= 905&& \text{simplify left side} \\[1 em]1000(1+2r+r^2) &= 905&& \\[1 em]1000+2000r+1000r^2 &= 905&& \\[1 em]1000r^2+2000r+1000 &= 905&& \text{move all terms to the left hand side } \\[1 em]1000r^2+2000r+1000-905 &= 0&& \text{simplify left side} \\[1 em]1000r^2+2000r+95 &= 0&& \\[1 em] \end{aligned} $$
$ 1000x^{2}+2000x+95 = 0 $ is a quadratic equation.
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