Answer:
[tex]m=\cfrac{\sqrt{73}\pm 7 }{4}[/tex]
Step-by-step explanation:
[tex]2m^2\:-\:7m\:-\:13\:=\:-10[/tex]
We'll use Quadratic formula to solve this equation:
[tex]\cfrac{-b\pm \sqrt{b^2-4ac} }{2a}[/tex]
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[tex]2m^2-7m-13=-10[/tex]
→ Add 10 from both sides:
[tex]-13-(-10)=-10-(-10)[/tex]
→ Subtract -10 from -10= 0
[tex]2m^2-7m-13-(10)=0[/tex]
→ Subtract -10 from -13:
Now, Equation is in standard from ax^2+bx+c=0, we'll solve it using Quadratic formula:
[tex]\cfrac{-b\pm \sqrt{b^2-4ac} }{2a}[/tex]
[tex]m=\cfrac{-\left(-7\right)\pm \sqrt{\left(-7\right)^2-4\times \:2\left(-3\right)}}{2\times \:2}[/tex]
Square -7, you'll get 49, multiply -4 * 2= 8, and than -8 * -3= 24
[tex]m=\cfrac{-(-7)\pm \sqrt{49+24} }{2\times 2}[/tex]
→ Add 49 + 24= 73
[tex]m=\cfrac{-(-7)\pm \sqrt{73} }{2\times 2}[/tex]
[tex]m=\cfrac{7\pm\sqrt{73} }{2\times 2}[/tex]
→ Multiply 2 * 2= 4
[tex]m=\cfrac{\sqrt{73}\pm 7 }{4}[/tex]
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