Question

Write -4x+2" align="absmiddle" class="latex-formula"> in the form of $a(x+p) ^{2} +q$ and solve

Answer 1

Because the coefficient of x^2 is -1, we know that a will be -1.  Knowing that the coefficient of x is -4, we can calculate that p=2.  Thus, we have -1(x+2)^2+q is our equation.  This is equal to -x^2-4x-4+q.  As the constant term must be 2, we can then see that q is 6.

As such, we have -1(x+2)^2+6=0 as our factorization.

To solve this equation, we can use the quadratic formula.  Plugging in values, we have:

$\frac{4+-2 \sqrt{6} }{-2}$
which is equal to: (when the fraction is simplified)
$-2+- \sqrt{6}$