Algebra - Quadratic Equations

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Section 2.6 : Quadratic Equations - Part II

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11. Use the quadratic formula to solve the following quadratic equation.

\[8{u^2} + 5u + 70 = 5 - 7u\]

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First, we need to get the quadratic equation in standard form. This is,

\[8{u^2} + 12u + 65 = 0\] Show Step 2

Now we need to identify the values for the quadratic formula.

\[a = 8\hspace{0.25in}b = 12\hspace{0.25in}c = 65\] Show Step 3

Plugging 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 : \[\require{bbox} \bbox[2pt,border:1px solid black]{{u = \frac{{ - 3}}{4} - \frac{{11}}{4}i\,\,{\mbox{and }}u = \frac{{ - 3}}{4} + \frac{{11}}{4}i}}\] .