Solve for x x+10/x=7

Problem

x+10/x=7

Solution

1. Multiply the entire equation by x to eliminate the fraction, assuming x≠0

x2+10=7*x

2. Rearrange the equation into standard quadratic form a*x2+b*x+c=0 by subtracting 7*x from both sides.

x2−7*x+10=0

3. Factor the quadratic expression by finding two numbers that multiply to 10 and add to −7

(x−2)*(x−5)=0

4. Apply the zero product property by setting each factor equal to zero.

x−2=0

x−5=0

5. Solve for x in each linear equation.

x=2

x=5

Final Answer

x=2,5

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