What is x if −8=13x+x?

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Belen Hebert · Accepted Answer

You have two solutions: x=−4−473, and x=−4+473 Explanation: First of all, note that x can&#039;t be zero, otherwise 13x would be a division by zero. So, provided x≠0, we can rewrite the equation as 3x3x−8=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 x≠0, 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±b2−4ac2a where a, b and c play the role of ax2+bx+c=0. So, the solving formula becomes −24±242−4⋅3⋅12⋅3 −24±576−126 −24±5646 Since 564=36⋅473, we can simplfy it out the square root, obtaining −24±64736 and finally we can simplify the whole expression: −⧸6⋅4±⧸6473⧸6 into −4±473

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

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