solve the following equation by completing the square
x(square) -13x + 21 = 0
Then x= or x=
x^2-13x+21 = 0
x^2-13x+(13/2)^2 + 21 - (13/2)^2 = 0
(x - 13/2)^2 - 85/4 = 0
x - 13/2)^2 = 85/4
x - 13/2 = ±√85/2
x = (13±√85)/2
To solve the equation x^2 - 13x + 21 = 0 by completing the square, follow these steps:
Step 1: Move the constant term to the other side of the equation:
x^2 - 13x = -21
Step 2: Take half of the coefficient of x, square it, and add it to both sides of the equation. This step is called completing the square:
x^2 - 13x + (-13/2)^2 = -21 + (-13/2)^2
x^2 - 13x + 169/4 = -21 + 169/4
Step 3: Simplify the equation:
x^2 - 13x + 169/4 = -84/4 + 169/4
x^2 - 13x + 169/4 = 85/4
Step 4: Rewrite the left side of the equation as a perfect square:
(x - 13/2)^2 = 85/4
Step 5: Take the square root of both sides of the equation:
√(x - 13/2)^2 = ± √(85/4)
Step 6: Solve for x:
x - 13/2 = ± √(85/4)
Step 7: Add 13/2 to both sides of the equation:
x = 13/2 ± √(85/4)
Therefore, x = (13 + √85)/2 or x = (13 - √85)/2.