Problem Solving

If (x + 2)^2 = − 4 + 10x , then which of the following could be the value of x?

A) 2
B) 1
C) 0
D) −1
E) −2
OA is a
Can anyone help me with the solution to this question? Thank you for your help

If (x + 2)^2 = - 4 + 10x , then which of the following could be the value of x?

A) 2
B) 1
C) 0
D) -1
E) -2
OA is a
Can anyone help me with the solution to this question? Thank you for your help

Hi Roland2rule,
Let's take a look at your question.

$$\left(x+2\right)^2=-4+10x$$
Evaluate Left hand side,
$$x^2+4x+4=-4+10x$$
$$x^2+4x+4+4-10x=0$$
$$x^2+4x-10x+4+4=0$$
$$x^2-6x+8=0$$

Let's now factorize it by grouping method,
$$x^2-4x-2x+8=0$$
$$x\left(x-4\right)-2\left(x-4\right)=0$$
$$\left(x-2\right)\left(x-4\right)=0$$
$$\left(x-2\right)=0,\ \left(x-4\right)=0$$
$$x=2,\ 4$$

Therefore, by factorizing, we got two values of x i.e. 2 and 4.

But in the given options we can only find 2, therefore Option A is correct.

Hope it helps.
I am available if you'd like any followup.