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

Question

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

0

Answers ( No )

    0
    2021-09-10T03:36:53+00:00

    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

    0
    2021-09-10T03:37:04+00:00

    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}

Leave an answer

Browse
Browse