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k\left(k+7\right)
Factor out k.
k^{2}+7k=0
Quadratic polynomial can be factored using the transformation ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right), where x_{1} and x_{2} are the solutions of the quadratic equation ax^{2}+bx+c=0.
k=\frac{-7±\sqrt{7^{2}}}{2}
All equations of the form ax^{2}+bx+c=0 can be solved using the quadratic formula: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. The quadratic formula gives two solutions, one when ± is addition and one when it is subtraction.
k=\frac{-7±7}{2}
Take the square root of 7^{2}.
k=\frac{0}{2}
Now solve the equation k=\frac{-7±7}{2} when ± is plus. Add -7 to 7.
k=0
Divide 0 by 2.
k=-\frac{14}{2}
Now solve the equation k=\frac{-7±7}{2} when ± is minus. Subtract 7 from -7.
k=-7
Divide -14 by 2.
k^{2}+7k=k\left(k-\left(-7\right)\right)
Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute 0 for x_{1} and -7 for x_{2}.
k^{2}+7k=k\left(k+7\right)
Simplify all the expressions of the form p-\left(-q\right) to p+q.