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

Answer: A) x=-8±5$\sqrt{2}$

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±$\sqrt{144+56}$)/2

u=(-12±$\sqrt{200}$)/2              

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

u=(-12±10$\sqrt{2}$)/2

u=-6±5$\sqrt{2}$

and finally:

x=u-2

x=-6±5$\sqrt{2}$-2

x=-8±5$\sqrt{2}$

Answer 2

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