Solve 7k^2-42k

$$7 k ^ { 2 } - 42 k$$

Factor

$$7k\left(k-6\right)$$

Solution Steps

Factor out 7.

$$7\left(k^{2}-6k\right)$$

Consider k^{2}-6k. Factor out k.

$$k\left(k-6\right)$$

Rewrite the complete factored expression.

$$7k\left(k-6\right)$$

Steps Using the Quadratic Formula

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.

$$7k^{2}-42k=0$$

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.

$$k=\frac{-\left(-42\right)±\sqrt{\left(-42\right)^{2}}}{2\times 7}$$

Take the square root of \left(-42\right)^{2}.

$$k=\frac{-\left(-42\right)±42}{2\times 7}$$

The opposite of -42 is 42.

$$k=\frac{42±42}{2\times 7}$$

Multiply 2 times 7.

$$k=\frac{42±42}{14}$$

Now solve the equation k=\frac{42±42}{14} when ± is plus. Add 42 to 42.

$$k=\frac{84}{14}$$

Divide 84 by 14.

$$k=6$$

Now solve the equation k=\frac{42±42}{14} when ± is minus. Subtract 42 from 42.

$$k=\frac{0}{14}$$

Divide 0 by 14.

$$k=0$$

Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute 6 for x_{1} and 0 for x_{2}.

$$7k^{2}-42k=7\left(k-6\right)k$$

Evaluate

$$7k\left(k-6\right)$$