Question

Solve (x-8)(4x+2)= 0 using the Zero Property

Answer 1

Explanation:

`\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`
`\mathrm{Solve\:}\:4x+2=0:\quad x=-(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\\(4x)/(4)=(-2)/(4)`

`Simplify\\(4x)/(4)=(-2)/(4)\\\mathrm{Simplify\:}(4x)/(4):\quad x\\(4x)/(4)\\\mathrm{Divide\:the\:numbers:}\:(4)/(4)=1\\=x`

`\mathrm{Simplify\:}(-2)/(4):\quad -(1)/(2)\\(-2)/(4)\\\mathrm{Apply\:the\:fraction\:rule}:\quad (-a)/(b)=-(a)/(b)\\=-(2)/(4)\\\mathrm{Cancel\:the\:common\:factor:}\:2\\=-(1)/(2)\\x=-(1)/(2)\\The\:solutions\:to\:the\:quadratic\:equation\:are:\\x=8,\:x=-(1)/(2)`

Answer 2

x = 8 or x = -1/2

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