Q:

Use the quadratic formula to solve x2 + 9x + 10 = 0.What are the solutions to the equation?

Accepted Solution

A:
Answer:[tex]\large\boxed{x=\dfrac{-9\pm\sqrt{41}}{2}}[/tex]Step-by-step explanation:[tex]\text{The quadratic formula of}[/tex][tex]ax^2+bx+c=0[/tex][tex]\text{If}\ b^2-4a<0,\ \text{then the equation has no solution}\\\\\text{If}\ b^2-4ac=0,\ \text{then the equation has one solution}\ x=\dfrac{-b}{2a}\\\\\text{If}\ b^2-4ac>0,\ \text{then the equation has two solutions}\ x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}\\=========================================[/tex][tex]\text{We have}\ x^2+9x+10=0\\\\a=1,\ b=9,\ c=10\\\\\text{substitute:}\\\\b^2-4ac=9^2-4(1)(10)=81-40=41>0\qquad _{\text{two solutions}}\\\\\sqrt{b^2-4ac}=\sqrt{41}\\\\x=\dfrac{-9\pm\sqrt{41}}{2(1)}=\dfrac{-9\pm\sqrt{41}}{2}[/tex]