To determine how to solve the given equation \( x^2 - 6 = \frac{3}{2}x + 2 \), let's follow a detailed, step-by-step solution:
1. Identify the Type of Equation:
The given equation is:
[tex]\[ x^2 - 6 = \frac{3}{2}x + 2 \][/tex]
This resembles a quadratic equation because it has a term with \( x^2 \).
2. Reframe the Equation into Standard Form:
To solve the equation, we need to reframe it into a standard quadratic form \( ax^2 + bx + c = 0 \).
Move all terms to one side of the equation:
[tex]\[ x^2 - 6 - \frac{3}{2}x - 2 = 0 \][/tex]
Simplify the terms:
[tex]\[ x^2 - \frac{3}{2}x - 8 = 0 \][/tex]
3. Conclusion:
The equation is now in standard quadratic form:
[tex]\[ x^2 - \frac{3}{2}x - 8 = 0 \][/tex]
To solve this quadratic equation, you would typically use techniques such as factoring, completing the square, or applying the quadratic formula.
Considering this transformation and the nature of the resulting equation, the correct statement that describes how to solve the equation \( x^2 - 6 = \frac{3}{2}x + 2 \) is:
Square both sides and then solve the resulting quadratic equation.
