Question

algebra 2a semester online practice
complete this assessment to review what youve learned. it will not count toward your grade.

solve the quadratic equation ( x^2 - 4x = -10 ). which of the following expresses its solutions in the form ( a pm bi )?
(1 point)

( \bigcirc 2 pm isqrt{6} )

( \bigcirc -2 pm isqrt{6} )

( \bigcirc 4 pm 2isqrt{6} )

( \bigcirc 2 pm isqrt{14} )

Explanation:

Step1: Rewrite the equation

Rewrite the quadratic equation \(x^{2}-4x = - 10\) in standard form \(ax^{2}+bx + c=0\). Add 10 to both sides: \(x^{2}-4x + 10=0\).

Step2: Use completing the square

For the quadratic expression \(x^{2}-4x\), to complete the square, take half of the coefficient of \(x\) (which is \(- 4\)), square it. Half of \(-4\) is \(-2\), and \((-2)^{2}=4\).
So, \(x^{2}-4x+4=- 10 + 4\).
This simplifies to \((x - 2)^{2}=-6\).

Step3: Solve for x

Take the square root of both sides: \(x - 2=\pm\sqrt{-6}\).
Since \(\sqrt{-6}=\sqrt{6}\times\sqrt{-1}=i\sqrt{6}\), we have \(x=2\pm i\sqrt{6}\).

Answer:

\(2\pm i\sqrt{6}\) (corresponding to the option \(2\pm i\sqrt{6}\))