SOLVING QUADRATIC EQUATIONS:
3. x²+5x=-6, I'll use the quadratic formula for this one.
- x²+5x+6=0
- [tex]x = \frac{ - b \frac{ + }{} \sqrt{b {}^{2} - 4ac} }{2a} [/tex]
- [tex]x = \frac{ - 5 \frac{ + }{} \sqrt{5 {}^{2} - 4(1)(6)} }{2(1)} [/tex]
- [tex]x = \frac{ - 5 \frac{ + }{} \sqrt{25 - 24} }{2} = \frac{ - 5 \frac{ + }{} \sqrt{1} }{2} [/tex]
- [tex]x = \frac{ - 5 \frac{ + }{}1 }{2} [/tex]
- [tex]x = \frac{ - 5 + 1}{2} = \frac{ - 4}{2} \\ x = - 2[/tex]
- [tex]x = \frac{ - 5 - 1}{2} = \frac{ - 6}{2} \\ x = - 3[/tex]
checking: x=-2, x=-3
- x²+5x=-6
- (-2)²+5(-2)=-6
- 4-10=-6
- -6=-6, true
- x²+5x=-6
- (-3)²+5(-3)=-6
- 9-15=-6
- -6=-6, true
Therefore, the solutions of the equation x²+5x=-6 are x=-2, x=-3.
4. (x+1)(x-5)=0, I'll use the factoring method for this one.
- (x+1)(x-5)=0
- x+1=0, x-5=0
- x=-1, x=5
checking: x=-1, x=5
- (x+1)(x-5)=0
- (-1+1)(-1-5)=0
- (0)(-6)=0
- 0=0, true
- (x+1)(x-5)=0
- (5+1)(5-5)=0
- (6)(0)=0
- 0=0, true
Therefore, the solutions of the equation are x=-1, x=5.
5. x²+7x+10=0, I'll use the factoring method for this one.
- x²+7x+10=0
- (x+2)(x+5)=0
- x+2=0, x+5=0
- x=-2, x=-5
checking: x=-2, x=-5
- x²+7x+10=0
- (-2)²+7(-2)+10=0
- 4-14+10=0
- -10+10=0
- 0=0, true
- x²+7x+10=0
- (-5)²+7(-5)+10=0
- 25-35+10=0
- -10+10=0
- 0=0, true
Therefore, the solutions are x=-2, x=-5.
#CarryOnLearning
