Question

What are the solutions of the equation (x + 2)2 + 12(x + 2) - 14 = 0? Use u substitution and the quadratic formula to solve.

Answer 1

X^2+4x+4+12x+24-14=0

x^2+16x+14=0

x= -16 ± √(16)^2-4(1)(14) /2(1)

=-16± √200 /2

-16 ± 2√50 /2

-16 ± 10√2 /2

-8 ± 5√2

Answer 2

Answer: A) x=-8±5
`√(2)`

Step-by-step explanation: to find the solutions of the given equation, we need to use the substitution u=x+2, so the equation would now be:

`u^(2) +12u-14=0`

the quadratic formula is:

u=(-b±
`\sqrt{b^(2)-4ac }`)/2a

in this case a=1; b=12; and c=-14

so replacing the values it remains:

u=(-12±
`\sqrt{12^(2)-4*1*(-14) }`)/2*1

u=(-12±
`√(144+56)`)/2

u=(-12±
`√(200)`)/2

we can write 200 as 100*2 and the square root of 100 is 10:

u=(-12±10
`√(2)`)/2

u=-6±5
`√(2)`

and finally:

x=u-2

x=-6±5
`√(2)`-2

x=-8±5
`√(2)`