Question

Solve. Express your answer as exact roots
(d+1\2)^2+1

Answer 1

\((d+\frac{1}{2})^2 +1\)
First we FOIL: First, Outside, Inside, Last
First: \(d*d=d^2\)
Outside: \(d * \frac{1}{2} = \frac{d}{2}\)
Inside: \(\frac{1}{2} * d = \frac{d}{2}\)
Last: \(\frac{1}{2} * \frac{1}{2} = \frac{1}{4}\)
Add them all together to get: (hint: don't forget the +1 at the end.)
\(d^2 + \frac{d}{2} + \frac{d}{2} + \frac{1}{4} + 1 \)
Combine like terms:
\(\frac{d}{2} + \frac{d}{2} = \frac{2d}{2} = d\)
\(1 + \frac{1}{4} = \frac{4}{4} + \frac{1}{4} = \frac{5}{4}\)
\(d^2 + d + \frac{5}{4}\)
Now factor or use the quadratic equation:
\(\frac{b \pm \sqrt{b^2-4ac}}{2a}\)
\(ax^2 +bx + c\)
Substitute A, B, and C:
\(\frac{1 \pm \sqrt{1^2-4(1)(\frac{5}{4})}}{2(1)}\)
(hint: \(4 * 1 * \frac{5}{4} = \frac{20}{4} = 5\)
\(\frac{1 \pm \sqrt{1-5}}{2}\)
\(\frac{1 \pm \sqrt{-4}}{2}\)
\(\frac{1\pm2i}{2}\)
\(\frac{1+2i}{2} = \frac{3i}{2}\) or \(\frac{1-2i}{2} = \frac{-1i}{2}\)
Not exactly a pre-algebra question, unless you have entered it wrong.