Answer:
x = 8 or x = -1/2
Step-by-step explanation:
given:
(x-8)(4x+2)= 0
by zero property:
(x - 8) = 0
x = 8
or
(4x+2) = 0
4x = -2
x = -2/4
x = -1/2
Answer:
Step-by-step explanation:
[tex]\left(x-8\right)\left(4x+2\right)=0\\\mathrm{Using\:the\:Zero\:Factor\:Principle:\quad \:If}\:ab=0\:\mathrm{then}\:a=0\:\mathrm{or}\:b=0\:\left(\mathrm{or\:both}\:a=0\:\mathrm{and}\:b=0\right)\\\mathrm{Solve\:}\:x-8=0:\quad x=8\\x-8=0\\\mathrm{Add\:}8\mathrm{\:to\:both\:sides}\\x-8+8=0+8\\\mathrm{Simplify}\\x=8[/tex][tex]\mathrm{Solve\:}\:4x+2=0:\quad x=-\frac{1}{2}\\4x+2=0\\\mathrm{Subtract\:}2\mathrm{\:from\:both\:sides}\\4x+2-2=0-2\\\mathrm{Simplify}\\4x=-2\\\mathrm{Divide\:both\:sides\:by\:}4\\\frac{4x}{4}=\frac{-2}{4}[/tex]
[tex]Simplify\\\frac{4x}{4}=\frac{-2}{4}\\\mathrm{Simplify\:}\frac{4x}{4}:\quad x\\\frac{4x}{4}\\\mathrm{Divide\:the\:numbers:}\:\frac{4}{4}=1\\=x[/tex]
[tex]\mathrm{Simplify\:}\frac{-2}{4}:\quad -\frac{1}{2}\\\frac{-2}{4}\\\mathrm{Apply\:the\:fraction\:rule}:\quad \frac{-a}{b}=-\frac{a}{b}\\=-\frac{2}{4}\\\mathrm{Cancel\:the\:common\:factor:}\:2\\=-\frac{1}{2}\\x=-\frac{1}{2}\\The\:solutions\:to\:the\:quadratic\:equation\:are:\\x=8,\:x=-\frac{1}{2}[/tex]
