Question

Solve the equation: 12x^2-13x+4=13x^2-5x+1

Answer 1

`x = -4 +√(19) = 0.36 \\\\or\\\\x=-4 -√(19) =-8.36`

Explanation:

`12x^2-13x+4=13x^2-5x+1\\\\\implies 12x^2-13x+4-13x^2+5x-1 = 0\\\\\implies -x^2-8x+3= 0\\\\\implies x^2+8x-3= 0\\`

This is of the form ax² + bx + c = 0

Where a = 1, b = 8 and c = -3

Using the quadratic formula:

`x=(-b\pm√(b^2 - 4ac) )/(2a)`

we have:

`x=(-8\pm√(8^2 - 4(-3)) )/(2)\\\\= (-8\pm√(64 + 12) )/(2)\\\\= (-8\pm√(76) )/(2)\\\\= (-8\pm2√(19) )/(2)\\\\= -4\pm√(19)`

`x = -4 +√(19) \;\;\;or\;\;\; x = -4 -√(19)\\\\x = -4 +4.36 \;\;\;or\;\;\; x = -4 -4.36\\\\x = 0.36 \;\;\;or\;\;\; x=-8.36`

Answer 2

Explanation:

12x^2-13x+4=13x^2-5x+1

by solving it we get

x^2 + 8x - 3 =0

by quadratic formula

x=(-8+-
`√(64+12)`)/2

x= -4+-
`\sqrt{66\\`/2