To solve the equation x^2 - 9x - 4 = 6 using completing the square method, follow these steps:
Step 1: Add 4 to both sides of the equation to isolate the x^2 term on the left side:
x^2 - 9x - 4 + 4 = 6 + 4
This simplifies to:
x^2 - 9x = 10
Step 2: To complete the square, take half of the coefficient of the x-term (-9) and square it. Half of -9 is -9/2, and (-9/2)^2 is (81/4).
Add (81/4) to both sides of the equation:
x^2 - 9x + (81/4) = 10 + (81/4)
This simplifies to:
x^2 - 9x + (81/4) = 41/2
Step 3: Now, the left side of the equation can be written as a perfect square:
(x - 9/2)^2 = 41/2
Step 4: Take the square root of both sides of the equation to solve for x. Don't forget that the square root has both positive and negative solutions:
β(x - 9/2)^2 = Β±β(41/2)
Simplifying further:
x - 9/2 = Β±β(41/2)
Step 5: Solve for x by adding 9/2 to both sides of the equation:
x = 9/2 Β± β(41/2)
Therefore, the solutions to the equation x^2 - 9x - 4 = 6 using the completing the square method are:
x = 9/2 + β(41/2)
x = 9/2 - β(41/2)