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

What are the solutions of the equation (x + 2)2 + 12(x + 2) - 14 = 0? Use u substitution-example-1
User Atm
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2 Answers

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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

User Eboubaker
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7.7k points
3 votes

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)

User Steve Evans
by
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