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

Answer = A) 2

\(x^2 + 4x + 4 = -4 + 10x\)

\(x^2 - 6x + 8 = 0\)

(x - 4)(x - 2) = 0

x = 4 OR x = 2

Solve equation to get x^2-6x+8 = 0 which has solutions x=4 or x=2.
Answer is A.

Backsolving

The key to using backsolving is to use the answer choices and see if they work. In this respect, backsolving is like picking numbers except that the numbers we pick are one or more of the actual answer choices. Look for the answer which makes both sides equal. In this particular problem, we may choose to start testing on any single answer choice. Choice A is as good a starting point as any.

Choice A.
(2 + 2)2 = −4 + 10(2)
16 = 16; This is the correct answer since both sides are equal.

Choice B.
(1 + 2)2 = −4 + 10(1); 9 = 6. This is a wrong answer since both sides are not equal.

Choice C.
(0 + 2)2 = −4 + 10(0); 4 = −4. This is a wrong answer since both sides are not equal.

Choice D.
(−1 + 2)2 = −4 + 10(−1); 1 = −14. This is a wrong answer since both sides are not equal.

Choice E.
(−2 + 2)2 = −4 + 10(−2); 0 = −24. This is a wrong answer since both sides are not equal.

Answer: A.

Simply expand (x+2)^2 and combine all terms on one side of the equation: x^2 + 4x + 4 = -4 + 10x, yielding x^2 -6x + 8=0. The two solutions are 2 and 4.

Choice A

We can simplify the given equation and factor the result:

x^2 + 4x + 4 = -4 + 10x

x^2 - 6x + 8 = 0

(x - 4)(x - 2) = 0

x = 4 or x = 2

Alternate Solution:

Let’s substitute each value in the answer choices for x until we find a value that satisfies the given equation:

A) x = 2

Is (2 + 2)^2 = -4 + 10(2) ?

Is 4^2 = -4 + 20 ?

Is 16 = 16? Yes.

Answer: A

\(x^2 + 4 + 4x = -4 + 10x\)

Or, \(x^2 -6x + 8 = 0\)

Or, \(x^2 -4x -2x + 8 = 0\)

Or, \(x(x-4) -2(x-4) = 0\)

Or, \((x-2)(x-4) = 0\)

So, \(x = 2\) or \(x = 4\)

Among the given options, only(A) satisfies, hence, correct answer must be (A)

Hi All,

While this question can be solved Algebraically, we're told that one of the numbers IS a solution to the equation - so we can also solve it by TESTing THE ANSWERS. Once we find an answer that 'fits', we can stop working.

Let's start with Answer A: 2... IF X=2, then we have (4)^2 = -4 +2(10).... 16 = 16. Since the equation 'balances', this must the answer.

Final Answer:

GMAT assassins aren't born, they're made,
Rich

(x+2)(x+2) = -4 + 10x
x^2 +4x+4 = -4 + 10x
x^2 -6x +8 = 0
(x-2)(x-4)
x =2 or 4