Question

Complete the square for this equation that has coefficients of its terms as variables: ax^2 + bx + c = 0. What is the final line of the calculation?

a) x = (-b ±√(b^2 - 4ac)) / (2a)
b) x^2 + (b/a)x + (c/a) = 0
c) x = (-b ± √(b^2 + 4ac)) / (2a)
d) x^2 + (b/a)x - (c/a) = 0

Answer 1

To complete the square for the quadratic equation ax^2 + bx + c = 0, divide the equation by 'a', move 'c' to the other side, add the square of half of 'b', factor as a perfect square trinomial, and solve for 'x'. The final equation is x = (-b ± √(b^2 - 4ac)) / (2a).

Step-by-step explanation:

To complete the square for the given quadratic equation ax^2 + bx + c = 0, follow these steps:

1. Divide the entire equation by the coefficient 'a' to make the leading coefficient 1.
2. Move the constant term 'c' to the other side of the equation.
3. Take half of the coefficient 'b' and square it: (b/2)^2.
4. Add the square obtained in step 3 to both sides of the equation.
5. Factor the left side of the equation as a perfect square trinomial.
6. Solve for 'x' by taking the square root of both sides of the equation.

The final equation, after completing the square, is in the form: x = (-b ± √(b^2 - 4ac)) / (2a). Therefore, the correct answer is a) x = (-b ± √(b^2 - 4ac)) / (2a).