Let's solve your equation step-by-step.<span><span><span>4<span>x2</span></span>+<span>2<span><span>(<span><span>2x</span>+2</span>)</span>2</span></span></span>=100</span>Step 1: Simplify both sides of the equation.<span><span><span><span>12<span>x2</span></span>+<span>16x</span></span>+8</span>=100</span>Step 2: Subtract 100 from both sides.<span><span><span><span><span>12<span>x2</span></span>+<span>16x</span></span>+8</span>−100</span>=<span>100−100</span></span><span><span><span><span>12<span>x2</span></span>+<span>16x</span></span>−92</span>=0</span>Step 3: Use quadratic formula with a=12, b=16, c=-92.<span>x=<span><span><span>−b</span>±<span>√<span><span>b2</span>−<span><span>4a</span>c</span></span></span></span><span>2a</span></span></span><span>x=<span><span><span>−<span>(16)</span></span>±<span>√<span><span><span>(16)</span>2</span>−<span><span>4<span>(12)</span></span><span>(<span>−92</span>)</span></span></span></span></span><span>2<span>(12)</span></span></span></span><span>x=<span><span><span>−16</span>±<span>√4672</span></span>24</span></span><span><span>x=<span><span><span>−2</span>3</span>+<span><span><span><span>13</span><span>√73</span></span><span> or </span></span>x</span></span></span>=<span><span><span>−2</span>3</span>+<span><span><span>−1</span>3</span><span>√73</span></span></span></span>Answer:<span><span>x=<span><span><span>−2</span>3</span>+<span><span><span><span>13</span><span>√73</span></span><span> or </span></span>x</span></span></span>=<span><span><span>−2</span>3</span>+<span><span><span>−1</span>3</span><span>√<span>73</span></span></span></span></span>
From the question, we are informed that the depth of the water in the pool changes by −3/4 foot every hour and that the depth of the water was 5 feet when she started draining.
