# Chapter R - Algebra Reference - R.4 Equations - R.4 Exercises - Page R-16: 19

$\displaystyle \frac{2+\sqrt{10}}{2}\approx 2.581$ $\displaystyle \frac{2-\sqrt{10}}{2}\approx-0.581$

#### Work Step by Step

Set the $RHS$ to 0 by subtracting 3 from both sides $2m^{2}-4m=3\qquad.../-3$ $2m^{2}-4m-3=0$ To factor the trinomial we search for integer factors of $2\times(-3)=-6$ whose sum is $-4$ ... ... none We can always use the quadratic formula: (For $ax^{2}+bx+c=0,\ x=\displaystyle \frac{-b\pm\sqrt{b^{2}-4ac}}{2a}$ ) $m=\displaystyle \frac{-(-4)\pm\sqrt{(-4)^{2}-4(2)(-3)}}{2(2)}$ $=\displaystyle \frac{4\pm\sqrt{40}}{4}=\frac{4\pm\sqrt{4\times 10}}{4}$ $=\displaystyle \frac{4\pm 2\sqrt{10}}{4}=\frac{2(2\pm\sqrt{10})}{2(2)}$ $m=\displaystyle \frac{2\pm\sqrt{10}}{2}$ Solutions: $\displaystyle \frac{2+\sqrt{10}}{2}\approx 2.581$ and $\displaystyle \frac{2-\sqrt{10}}{2}\approx-0.581$.

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