Using the completing the square method solve :
4x^2 - 5x -8 = 0
To solve the equation using the completing the square method, we can follow these steps:
1. Move the constant term to the other side of the equation:
4x^2 - 5x = 8
2. Divide the entire equation by the coefficient of x^2 (which is 4 in this case) to make the leading coefficient 1:
x^2 - (5/4)x = 2
3. Take half of the coefficient of x (-5/4), square it, and add it to both sides of the equation:
x^2 - (5/4)x + (-5/8)^2 = 2 + (-5/8)^2
x^2 - (5/4)x + 25/64 = 2 + 25/64
4. Simplify the right side of the equation:
x^2 - (5/4)x + 25/64 = 128/64 + 25/64
x^2 - (5/4)x + 25/64 = 153/64
5. Factor the left side of the equation as a perfect square:
(x - 5/8)^2 = 153/64
6. Take the square root of both sides of the equation:
x - 5/8 = ±√(153/64)
7. Solve for x by adding 5/8 to both sides:
x = 5/8 ± √(153/64)
Therefore, the solutions to the equation 4x^2 - 5x - 8 = 0 using the completing the square method are:
x = 5/8 + √(153/64)
x = 5/8 - √(153/64)