# Chapter 10 - Quadratic Equations - 10.1 - Quadratic Equations - Problem Set 10.1 - Page 442: 50

{$\frac{-3- 4\sqrt {2}}{5},\frac{-3+4\sqrt {2}}{5}$}

#### Work Step by Step

Using Property 10.1, which states that for any non-negative real number $a$, $x^{2}=a$ can be written as $x=\pm\sqrt a$, we obtain: Step 1: $(5x+3)^{2}=32$ Step 2: $5x+3=\pm \sqrt {32}$ Step 3: $5x+3=\pm \sqrt {16\times2}$ Step 4: $5x+3=\pm \sqrt {4^{2}\times2}$ Step 5: $5x+3=\pm 4\sqrt {2}$ Step 6: $5x+3=+ 4\sqrt {2}$ or $5x+3=-4 \sqrt {2}$ Step 7: $5x=-3+ 4\sqrt {2}$ or $5x=-3-4 \sqrt {2}$ Step 8: $x=\frac{-3+ 4\sqrt {2}}{5}$ or $x=\frac{-3- 4\sqrt {2}}{5}$ The solution set is {$\frac{-3- 4\sqrt {2}}{5},\frac{-3+4\sqrt {2}}{5}$}.

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