Final answer:
To rewrite the equation g(x)=2x²-7x+5 by completing the square, divide by the coefficient of x², move the constant term to the other side, add (b/2a)² to both sides, factor as a square of a binomial, and solve for x.
Step-by-step explanation:
To rewrite the quadratic equation g(x)=2x²-7x+5 by solving the square (completing the square), we need to express it in the form of (ax+b)²=c. First, we divide every term by the coefficient of the x² term if it's not 1 (which in this case it is 2), then move the constant term to the other side of the equation, find the value that completes the square for the x terms, add it to both sides, factor the left side as a square of a binomial, and finally solve for x.
Divide by the coefficient of x²:
To complete the square, add (b/2a)² to both sides:
- x²- (7/2)x + (7/4)² = 5/2 + (7/4)²
Factor the perfect square trinomial:
Now, simplify the right side and solve for x:
- (x - 7/4)² = 98/16 + 49/16
- (x - 7/4)² = 147/16
- x - 7/4 = ±√(147/16)
- x = 7/4 ± √(147/16)
Which gives us the values of x that satisfy the equation g(x).