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pishuonlain [190]
3 years ago
8

x^2+1/2x+1/16=4/9 Factor the perfect-square trinomial on the left side of the equation. (x + )² = 4/9

Mathematics
2 answers:
viva [34]3 years ago
8 0

Answer:

\frac{1}{4}

Step-by-step explanation:

we have

x^{2} +\frac{1}{2}x+\frac{1}{16}=\frac{4}{9}

we know that

(x+a)^{2}=x^{2}+2ax+a^{2}

in this problem

2ax=\frac{1}{2}x ------> a=\frac{1}{4}

a^{2}=\frac{1}{16} -----> a=\frac{1}{4}

so

x^{2} +\frac{1}{2}x+\frac{1}{16}=(x+\frac{1}{4})^{2}

the missing number in the left side is \frac{1}{4}


Nezavi [6.7K]3 years ago
5 0
The missing number is the square-root of the constant term on the left-hand-side, which equals sqrt(1/16)=1/sqrt(16)=1/4.
Check:
(x+1/4)^2=x^2+2*(1/4)x+(1/4)^2=x^2+x/2+1/16.   ok

Answer: x= 1/4
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