Consider the equation: x^2+14x+24=0 A) First, use the "completing the square" process , to write this equation in the form (x+D)^2=E and enter your results below. x^2+14x+24=0 is equivalent to: square = square Preview left side of eqn: B) Solve your equation and enter your answers below as a list of numbers , separated with a comma where necessary. Answer(s): square

) To complete the square for the equation $x^{2}+14x+24=0$, we need to rewrite it in the form $(x+D)^{2}=E$.<br /><br />First, let's isolate the $x$ terms on one side of the equation:<br />$x^{2}+14x=-24$<br /><br />Next, we need to add a constant term to both sides of the equation to complete the square. This constant term is given by $(\frac{b}{2})^2$, where $b$ is the coefficient of the $x$ term.<br /><br />In this case, $b=14$, so $(\frac{b}{2})^2 = (\frac{14}{2})^2 = 49$.<br /><br />Adding 49 to both sides of the equation, we get:<br />$x^{2}+14x+49=-24+49$<br />$x^{2}+14x+49=25$<br /><br />Now, we can rewrite the left side of the equation as a perfect square:<br />$(x+7)^{2}=25$<br /><br />So, the equation $x^{2}+14x+24=0$ is equivalent to:<br />$(x+7)^{2}=25$<br /><br />B) To solve the equation $(x+7)^{2}=25$, we need to take the square root of both sides:<br /><br />$x+7=\pm\sqrt{25}$<br />$x+7=\pm5$<br /><br />Solving for $x$, we get:<br />$x=-7+5$ or $x=-7-5$<br />$x=-2$ or $x=-12$<br /><br />Therefore, the solutions to the equation $x^{2}+14x+24=0$ are $x=-2$ and $x=-12$.