Question

How to solve 2x²-x-21=0 using completing the square?

a) x=(1±√169)/4
b) x=(-1±√169)/4
c) x=(1±√85)/4
d) x=(-1±√85)/4

Answer 1

To solve the quadratic equation 2x²-x-21=0 using completing the square, divide by the leading coefficient, rearrange, add the square of half the linear coefficient to both sides, simplify, and then take the square root of both sides to find the solutions.

To solve the quadratic equation 2x²-x-21=0 by completing the square, you would follow these steps:

1. Divide all terms by 2, the coefficient of x², to simplify the equation to x² - (1/2)x - (21/2) = 0.
2. Rearrange the equation to isolate the constant term: x² - (1/2)x = (21/2).
3. Add the square of half the coefficient of x to both sides to complete the square: x² - (1/2)x + (1/8)² = (21/2) + (1/8)².
4. Simplify and solve the resulting perfect square trinomial on the left side of the equation and simplify the right side.
5. Finally, take the square root of both sides and solve for x, which will give you two solutions.

The correct answer is not provided in the options, as this process will lead to different solutions than those listed. The process shown in the question itself uses different numbers and methods.