Question

Marika solved the equation (6x + 15)2 + 24 = 0. Her work is below. 1. (6x + 15)2 = –24 2. = 3. 6x + 15 = 4. 6x = – 15 5. x = Analyze Marika’s steps. Which statement is true about her work? In step 2, Marika should have simplified to be . There are no real solutions to this equation because the square root of a negative number is not a real number. There should be two real solutions to this equation because = . Marika correctly solved this equation.

Answer 1

The answer would be B, there are no real solutions to the secretion because the Square root of a negative number is not a real number.

Answer 2

Given equation: $(6x + 15)^2 + 24 = 0.$

First step Marika applied to get rid 24 from left side.

24 is added on left side of the equation.

The reverse operation of addition is subtract.

So, we need to subtract 24 from both sides in first step.

$(6x + 15)^2 + 24-24 = 0-24$

On simplifying it gives:

$(6x+15)^2= -24.$.

Then she took square root to get rid square from left side .

But we can see that 24 is a negative number.

So, we can't take square root of 24.

Therefore, in second step the did some mistake:

There are no real solutions to this equation because the square root of a negative number is not a real number.