Solve k+64k^2

$$k + 64 k ^ { 2 }$$

Factor

$$k\left(64k+1\right)$$

Solution Steps

Factor out k.

$$k\left(1+64k\right)$$

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.

$$64k^{2}+k=0$$

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.

$$k=\frac{-1±\sqrt{1^{2}}}{2\times 64}$$

Take the square root of 1^{2}.

$$k=\frac{-1±1}{2\times 64}$$

Multiply 2 times 64.

$$k=\frac{-1±1}{128}$$

Now solve the equation k=\frac{-1±1}{128} when ± is plus. Add -1 to 1.

$$k=\frac{0}{128}$$

Divide 0 by 128.

$$k=0$$

Now solve the equation k=\frac{-1±1}{128} when ± is minus. Subtract 1 from -1.

$$k=-\frac{2}{128}$$

Reduce the fraction \frac{-2}{128} to lowest terms by extracting and canceling out 2.

$$k=-\frac{1}{64}$$

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 -\frac{1}{64} for x_{2}.

$$64k^{2}+k=64k\left(k-\left(-\frac{1}{64}\right)\right)$$

Simplify all the expressions of the form p-\left(-q\right) to p+q.

$$64k^{2}+k=64k\left(k+\frac{1}{64}\right)$$

Add \frac{1}{64} to k by finding a common denominator and adding the numerators. Then reduce the fraction to lowest terms if possible.

$$64k^{2}+k=64k\times \frac{64k+1}{64}$$

Cancel out 64, the greatest common factor in 64 and 64.

$$64k^{2}+k=k\left(64k+1\right)$$

Evaluate

$$k\left(64k+1\right)$$