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x^{2}+14x=0
Calculate -x to the power of 2 and get x^{2}.
x\left(x+14\right)=0
Factor out x.
x=0 x=-14
To find equation solutions, solve x=0 and x+14=0.
x^{2}+14x=0
Calculate -x to the power of 2 and get x^{2}.
x=\frac{-14±\sqrt{14^{2}}}{2}
This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 14 for b, and 0 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.
x=\frac{-14±14}{2}
Take the square root of 14^{2}.
x=\frac{0}{2}
Now solve the equation x=\frac{-14±14}{2} when ± is plus. Add -14 to 14.
x=0
Divide 0 by 2.
x=-\frac{28}{2}
Now solve the equation x=\frac{-14±14}{2} when ± is minus. Subtract 14 from -14.
x=-14
Divide -28 by 2.
x=0 x=-14
The equation is now solved.
x^{2}+14x=0
Calculate -x to the power of 2 and get x^{2}.
x^{2}+14x+7^{2}=7^{2}
Divide 14, the coefficient of the x term, by 2 to get 7. Then add the square of 7 to both sides of the equation. This step makes the left hand side of the equation a perfect square.
x^{2}+14x+49=49
Square 7.
\left(x+7\right)^{2}=49
Factor x^{2}+14x+49. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.
\sqrt{\left(x+7\right)^{2}}=\sqrt{49}
Take the square root of both sides of the equation.
x+7=7 x+7=-7
Simplify.
x=0 x=-14
Subtract 7 from both sides of the equation.