$$2x^2+9x+29 = (x-1)^2$$
Answer
$$ \begin{matrix}x_1 = -4 & x_2 = -7 \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} 2x^2+9x+29 &= (x-1)^2&& \text{simplify right side} \\[1 em]2x^2+9x+29 &= x^2-2x+1&& \text{move all terms to the left hand side } \\[1 em]2x^2+9x+29-x^2+2x-1 &= 0&& \text{simplify left side} \\[1 em]x^2+11x+28 &= 0&& \\[1 em] \end{aligned} $$
$ x^{2}+11x+28 = 0 $ is a quadratic equation.
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