I have been informed that on March 7th from 6:00am to 6:00pm Central Time Lamar University will be doing some maintenance to replace a faulty UPS component and to do this they will be completely powering down their data center.
Unfortunately, this means that the site will be down during this time. I apologize for any inconvenience this might cause.
Paul
February 18, 2026
Section 2.6 : Quadratic Equations - Part II
11. Use the quadratic formula to solve the following quadratic equation.
\[8{u^2} + 5u + 70 = 5 - 7u\]Show All Steps Hide All Steps
Start SolutionFirst, we need to get the quadratic equation in standard form. This is,
\[8{u^2} + 12u + 65 = 0\] Show Step 2Now we need to identify the values for the quadratic formula.
\[a = 8\hspace{0.25in}b = 12\hspace{0.25in}c = 65\] Show Step 3Plugging these into the quadratic formula gives,
\[u = \frac{{ - 12 \pm \sqrt {{{\left( {12} \right)}^2} - 4\left( 8 \right)\left( {65} \right)} }}{{2\left( 8 \right)}} = \frac{{ - 12 \pm \sqrt { - 1936} }}{{16}} = \frac{{ - 12 \pm 44i}}{{16}} = \frac{{ - 3 \pm 11i}}{4}\]The two solutions to this equation are then : \[\require{bbox} \bbox[2pt,border:1px solid black]{{u = \frac{{ - 3}}{4} - \frac{{11}}{4}i\,\,{\mbox{and }}u = \frac{{ - 3}}{4} + \frac{{11}}{4}i}}\] .