Can someone help.
Solve by completing the square.
x^2=5x+2
x^2 -5x -2 = 0
x^2 - 5x + (5/2)^2 -2 = (5/2)^2
(x- 5/2)^2 = 2 + 25/4 = 33/4
x - 5/2 = sqrt (33/4)
To solve the equation x^2 = 5x + 2 using completing the square method, you can follow these steps:
1. Begin by moving all terms to one side of the equation, so the equation becomes x^2 - 5x - 2 = 0.
2. Next, identify the coefficient of x which is -5 in this case. Divide it by 2, and then square the result. This will give you (-5/2)^2 = 25/4.
3. Add 25/4 to both sides of the equation to create perfect square trinomial. The equation becomes x^2 - 5x + 25/4 - 2 = 25/4.
4. Simplify the equation on the left side by combining like terms. The equation now becomes (x - 5/2)^2 - 2 = 25/4.
5. Add 2 to both sides of the equation to isolate the perfect square term. The equation becomes (x - 5/2)^2 = 25/4 + 2 = 33/4.
6. Finally, take the square root of both sides of the equation to solve for x. Remember to consider both positive and negative square roots. The equation becomes x - 5/2 = ±√(33/4).
Therefore, the solutions for x will be x = 5/2 ± √(33/4).