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

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.

Answer 2

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

What are word problems with algebraic equations?

Word problems with algebraic equations are methods with which we solve algebraic equations by breaking words into basic mathematical models by using variables and arithmetic operations.

From the given information, we are to identify the possible steps where mistakes occurred in Marika's calculations.

$\mathbf{(6x+15)^2 + 24 =0}$

Step 1:

Move 24 to the left-hand side.

$\mathbf{(6x+15)^2 =-24 }$

Taking the square root of both sides;

$\mathbf{(\sqrt{(6x+15)})^2 =\sqrt{-24} }$

$\mathbf{(6x+15) =\sqrt{-24} }$

But the square root of -24 is not 4, and due to the negative sign, the square root can not be determined.

Therefore, we can conclude that there are no real solutions to this equation because the square root of a negative number is not a real number.

Learn more about word problems with algebra here:

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