A quadratic equation is solved systematically by factoring to reveal its real roots clearly.

Solve:

\[ x^2-7x+10=0 \]

Solution:

\[ \text{Find two numbers that multiply to 10 and add to 7:} \] \[ x^2-5x-2x+10=0 \] \[ \text{Factor by grouping:} \] \[ x(x-5)-2(x-5)=0 \] \[ (x-5)(x-2)=0 \] \[ x=5 \text{ or } x=2 \]

Final Answer:

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\[ x=5,\; x=2 \]

Factoring reveals the quadratic roots efficiently.