What are the solutions of the equation (x + 2)2 + 12(x + 2) – 14 = 0? Use u substitution and the quadratic formula to solve.
2 answers:
(x + 2)²<span> + 12(x + 2) – 14 = 0
</span>(x +2) ² we use the formula (a+b)² = a² + 2ab + b²
<span>
(x</span>² + 2*2*x + 4 ) + (12*x + 12 * 2 ) - 14 = 0
(x² + 4x + 4) + (12x + 24) - 14 = 0
x² + 4x + 4 + 12x + 24 - 14 = 0
<span>we sort expressions
</span>x² + 4x + 12x + 4 + 24 - 14 = 0
<span>reduce
</span>x² + 16x + 14 = 0
a = 1 b = 16 c=14
Δ = b² - 4ac = 16² - 4*1*14 = 256 - 56 = 200
√Δ = √(2*10*10) = 10√2
Answer A
</span>(x +2) ² we use the formula (a+b)² = a² + 2ab + b²
<span>
(x</span>² + 2*2*x + 4 ) + (12*x + 12 * 2 ) - 14 = 0
(x² + 4x + 4) + (12x + 24) - 14 = 0
x² + 4x + 4 + 12x + 24 - 14 = 0
<span>we sort expressions
</span>x² + 4x + 12x + 4 + 24 - 14 = 0
<span>reduce
</span>x² + 16x + 14 = 0
a = 1 b = 16 c=14
Δ = b² - 4ac = 16² - 4*1*14 = 256 - 56 = 200
√Δ = √(2*10*10) = 10√2
Answer A
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I hope this helps you
