Question

Solve for the roots in simplest form using the quadratic formula:
4x2 – 12x = -5​

Answer 1

Answer:
`x=(5)/(2),\:x=(1)/(2)` or
`x=2.5,\:x=0.5`

Explanation:

`4x^2-12x=-5`

`\mathrm{Add\:}5\mathrm{\:to\:both\:sides}`

`4x^2-12x+5=-5+5`

`\mathrm{Simplify}`

`4x^2-12x+5=0`

Solve with Quadratic Formula

`x_(1,\:2)=(-b\pm √(b^2-4ac))/(2a)`

`a=4,\:b=-12,\:c=5:\quad x_(1,\:2)=(-\left(-12\right)\pm √(\left(-12\right)^2-4\cdot \:4\cdot \:5))/(2\cdot \:4)`

`(-\left(-12\right)+√(\left(-12\right)^2-4\cdot \:4\cdot \:5))/(2\cdot \:4)`

`\mathrm{Apply\:rule}\:-\left(-a\right)=a`

`(12+√(\left(-12\right)^2-4\cdot \:4\cdot \:5))/(2\cdot \:4)`

`12+√(\left(-12\right)^2-4\cdot \:4\cdot \:5)=12+√(64)`

`√(\left(-12\right)^2-4\cdot \:4\cdot \:5)=√(64)`

`√(64)=8`

`=(12+8)/(8)`

`=(20)/(8)`

`=(5)/(2)`

`x=(5)/(2),\:x=(1)/(2)`

Answer 2

x=2.5&.5

Explanation:

The quadratic formula is (-b+or-sqrt(b^2-4ac)/2a

12+or-sqrt((-12^2)-4(4)(5))

12+or-sqrt(144-80)

12+or-sqrt(64)

(12+8)/8 and (12-8)/8

x=2.5 and x=.5