Step 1

Given equation is \(\displaystyle{x}^{{{2}}}+{7}{x}+{10}={0}\).

To solve the given equation.

Solution:

Solving the given equation.

\(\displaystyle{x}^{{{2}}}+{7}{x}+{10}={0}\)

\(\displaystyle{x}^{{{2}}}+{5}{x}+{2}{x}+{10}={0}\)

x(x+5)+2(x+5)=0

(x+5)(x+2)=0

(x+5)=0 or (x+2)=0

x=-5 or x=-2

Therefore, solution is x=−5 or x=−2.

Step 2

Hence, required solution is x={-5, -2}.

Given equation is \(\displaystyle{x}^{{{2}}}+{7}{x}+{10}={0}\).

To solve the given equation.

Solution:

Solving the given equation.

\(\displaystyle{x}^{{{2}}}+{7}{x}+{10}={0}\)

\(\displaystyle{x}^{{{2}}}+{5}{x}+{2}{x}+{10}={0}\)

x(x+5)+2(x+5)=0

(x+5)(x+2)=0

(x+5)=0 or (x+2)=0

x=-5 or x=-2

Therefore, solution is x=−5 or x=−2.

Step 2

Hence, required solution is x={-5, -2}.