Algebra - Quadratic Equations

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Section 2.6 : Quadratic Equations - Part II

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

\[{x^2} - 6x + 4 = 0\]

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Start Solution

There really isn’t too much to this problem. First, we need to identify the values for the quadratic formula.

\[a = 1\hspace{0.25in}b = - 6\hspace{0.25in}c = 4\] Show Step 2

Plugging these into the quadratic formula gives,

\[x = \frac{{ - \left( { - 6} \right) \pm \sqrt {{{\left( { - 6} \right)}^2} - 4\left( 1 \right)\left( 4 \right)} }}{{2\left( 1 \right)}} = \frac{{6 \pm \sqrt {20} }}{2} = \frac{{6 \pm 2\sqrt 5 }}{2} = 3 \pm \sqrt 5 \]

The two solutions to this equation are then : \[\require{bbox} \bbox[2pt,border:1px solid black]{{x = 3 - \sqrt 5 \,\,{\mbox{and }}x = 3 + \sqrt 5 }}\] .