Question

-x^2=3x-6 using either completing the squares or quadratic formula

a) x=2,−1
b) x=3,−2
c) x=4,−3
d) x=1,−4

Answer 1

The quadratic equation -x^2 = 3x - 6 can be solved by rewriting it in the form x^2 + 3x - 6 = 0, and then applying the quadratic formula to find the solutions.

Step-by-step explanation:

The student's question, -x^2 = 3x - 6, asks for the solution to a quadratic equation, which can be found using either the completing the square method or the quadratic formula. First, we need to bring the equation into the standard quadratic form ax^2 + bx + c = 0. In this case, we need to move the terms to one side to get x^2 + 3x - 6 = 0.

Using the quadratic formula, -b ± √(b^2 - 4ac) over 2a, we substitute a = 1, b = 3, and c = -6 into the formula to find the roots. Simplifying under the radical gives us 9 + 24, which is 33. Therefore, the roots are obtained with -3 ± √33 over 2.