So for this, we will be completing the square to solve for m. Firstly, subtract 8 on both sides:
[tex]2m^2-16m=-8[/tex]
Next, divide both sides by 2:
[tex]m^2-8m=-4[/tex]
Next, we want to make the left side of the equation a perfect square. To find the constant of this perfect square, divide the m coefficient by 2, then square the quotient. In this case:
-8 ÷ 2 = -4, (-4)² = 16
Add 16 to both sides of the equation:
[tex]m^2-8m+16=12[/tex]
Next, factor the left side:
[tex](m-4)^2=12[/tex]
Next, square root both sides of the equation:
[tex]m-4=\pm \sqrt{12}[/tex]
Next, add 4 to both sides of the equation:
[tex]m=4\pm \sqrt{12}[/tex]
Now, while this is your answer, you can further simplify the radical using the product rule of radicals:
√12 = √4 × √3 = 2√3.
[tex]m=4\pm 2\sqrt{3}[/tex]
In exact form, your answer is [tex]m=4\pm \sqrt{12}\ \textsf{OR}\ m=4\pm 2\sqrt{3}[/tex]
In approximate form, your answers are (rounded to the hundreths) [tex]m=7.46, 0.54[/tex]
