Question

lesson 3 homework period____ the equation $x^{2}+9 = 3$ can be modeled by the graph shown below. use the graph for questions 1 and 2. 1. are the solutions to this equation real or imaginary? 2. how many solutions are there for this equation? determine the solution(s) for each of the following quadratic equations using the square roots method. 3. $7x^{2}-16 = 5x^{2}$ 4. $8x^{2}+12 = 3x^{2}+27$

Explanation:

for Question 1:

Step1: Simplify equation

\(x^2 = 3 - 9 = -6\)

Step2: Analyze square result

Square of real number ≥0, -6 <0

for Question 2:

Step1: Quadratic equation degree

Degree 2, has 2 solutions

Step2: Solutions type

Imaginary solutions exist

for Question 3:

Step1: Simplify equation

\(7x^2 - 5x^2 = 16\) → \(2x^2 = 16\)

Step2: Solve for \(x^2\)

\(x^2 = 8\)

Step3: Take square roots

\(x = \pm \sqrt{8} = \pm 2\sqrt{2}\)

for Question 4:

Step1: Simplify equation

\(8x^2 - 3x^2 = 27 - 12\) → \(5x^2 = 15\)

Step2: Solve for \(x^2\)

\(x^2 = 3\)

Step3: Take square roots

\(x = \pm \sqrt{3}\)

Answer:

for Question 1:
Imaginary