What is x if -8=\frac{1}{3x}+x?

Anabelle Schneider

Anabelle Schneider

Answered question

2022-02-04

What is x if 8=13x+x?

Answer & Explanation

Belen Hebert

Belen Hebert

Beginner2022-02-05Added 8 answers

You have two solutions:
x=4473, and
x=4+473
Explanation:
First of all, note that x can't be zero, otherwise 13x would be a division by zero. So, provided x0, we can rewrite the equation as
3x3x8=13x+x3x3x
24x3x=13x+3x23x
with the advantage that now all the terms have the same denominator, and we can sum the fractions:
24x3x=1+3x23x
Since we assumed x0, we can claim that the two fractions are equal if and only if the numerators are equal: so the equation is equivalent to
24x=1+3x2
which leads is to the quadratic equation
3x2+24x+1=0.
To solve this, we can use the classic formula
b±b24ac2a
where a, b and c play the role of ax2+bx+c=0.
So, the solving formula becomes
24±24243123
24±576126
24±5646
Since 564=36473, we can simplfy it out the square root, obtaining
24±64736
and finally we can simplify the whole expression:
64±64736
into 4±473

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