marika solved the equation (6x + 15)^2+24 = 0. her work is below. 1. (6x + 15)^2=-24 2. \\sqrt{(6x +…

marika solved the equation (6x + 15)^2+24 = 0. her work is below. 1. (6x + 15)^2=-24 2. \\sqrt{(6x + 15)^2}=\\sqrt{-24} 3. 6x + 15=-2\\sqrt{6} 4. 6x=-2\\sqrt{6}-15 5. x = \\frac{-2\\sqrt{6}-15}{6} analyze marikas steps. which statement is true about her work? in step 2, marika should have simplified \\sqrt{-24} to be 4\\sqrt{-6}. 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 \\sqrt{-24}=\\pm2\\sqrt{6}. marika correctly solved this equation.

marika solved the equation (6x + 15)^2+24 = 0. her work is below. 1. (6x + 15)^2=-24 2. \\sqrt{(6x + 15)^2}=\\sqrt{-24} 3. 6x + 15=-2\\sqrt{6} 4. 6x=-2\\sqrt{6}-15 5. x = \\frac{-2\\sqrt{6}-15}{6} analyze marikas steps. which statement is true about her work? in step 2, marika should have simplified \\sqrt{-24} to be 4\\sqrt{-6}. 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 \\sqrt{-24}=\\pm2\\sqrt{6}. marika correctly solved this equation.

Answer

Explanation:

Step1: Recall square - root property

The square of a real number (a), (a^2\geq0) for all real (a). In the equation ((6x + 15)^2=-24), the left - hand side ((6x + 15)^2) is a square of the real number (6x + 15) (assuming (x) is real), and the right - hand side is negative.

Step2: Analyze square root of negative number

The square root of a negative number, such as (\sqrt{-24}), is not a real number. In the set of real numbers, there is no number (y) such that (y^2=-24). So, the equation ((6x + 15)^2=-24) has no real solutions.

Answer:

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