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Write [tex](- x^{2}) -4x+2[/tex] in the form of [tex]a(x+p) ^{2} +q[/tex] and solve

Sagot :

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:

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