Consider 8x^2-48x=-104 Write the equation so that a=1;x^2+6 surd x=-13 COMPUTIII Complete the square: x^2-6x+9 surd =-13+9 √ Factor the trinomial and simplify (x+square )^2=

To solve the equation \(8x^2 - 48x = -104\), we first rewrite it in the standard quadratic form by moving all terms to one side:<br /><br />\[8x^2 - 48x + 104 = 0\]<br /><br />Next, we divide the entire equation by 8 to simplify:<br /><br />\[x^2 - 6x + 13 = 0\]<br /><br />Now, we want to complete the square. To do this, we need to isolate the constant term on one side of the equation:<br /><br />\[x^2 - 6x = -13\]<br /><br />To complete the square, we add \(\left(\frac{-6}{2}\right)^2 = 9\) to both sides:<br /><br />\[x^2 - 6x + 9 = -13 + 9\]<br /><br />Simplifying the right side, we get:<br /><br />\[x^2 - 6x + 9 = -4\]<br /><br />Now, we can factor the left side as a perfect square trinomial:<br /><br />\[(x - 3)^2 = -4\]<br /><br />So, the completed square form of the equation is:<br /><br />\[(x - 3)^2 = -4\]