Answer:
2 solutions: x= -1 x= [tex]\frac{1}{2}[/tex]
Step-by-step explanation:
You could solve this 2 ways, either by factoring or using the quadratic formula.
Factoring:
Use the formula: [tex]a^2-b^2=(a-b)(a+b)[/tex]
(4x+1-3)(3x+1+3)=0
(4x-2)(4x+4)=0
No we can factor out a 2 and a 4:
2(2x-1)4(x+1)=0
Divide both sides by 2x4:
(2x-1)(x+1)=0
Now set both equal to 0:
2x-1=0
x+1=0
x=[tex]\frac{1}{2}[/tex]
x=-1
For quadratic formula:
Use the formula: [tex](a+b)^2=a^2+2ab+b^2[/tex]
First expand the expression:
[tex]16x^2+8x-8=0[/tex]
Divide both sides by 2:
[tex]2x^2+x-1=0[/tex]
Now we can plug it in:
a=2
b=1
c=-1
[tex]x=\frac{-1+\sqrt{1^{2} -4(2)(-1)} }{4}[/tex]
[tex]x=\frac{-1+\sqrt{9} }{4}[/tex]
[tex]x=\frac{-1+3}{4}[/tex]
Now solve for each solution:
[tex]x=\frac{-1+3}{4} \\\\x=\frac{-1-3}{4} \\\\x=\frac{1}{2}\\x=-1[/tex]
Either way you get the same answer, hope this helps! :)
