x^2+bx+ ?=(x+ ? )^2.
To find the values of b and c in the expression x^2 + bx + c = (x + ?)^2, we can expand the squared binomial (x + ?)^2 and then compare the coefficients of the expanded expression to the original expression.
Expanding (x + ?)^2, we get:
(x + ?)^2 = x^2 + 2?x + ?^2
Now we will compare the coefficients. In the original expression x^2 + bx + c, the coefficient of x^2 is 1. So the coefficient of x^2 in the expanded expression (x + ?)^2 should also be 1. Comparing the coefficients, we have:
1 = 1
Next, let's compare the coefficients of x in both expressions. In the original expression x^2 + bx + c, the coefficient of x is b. So the coefficient of x in the expanded expression (x + ?)^2 should also be b. Comparing the coefficients, we have:
b = 2?
Finally, let's compare the constant terms in both expressions. In the original expression x^2 + bx + c, the constant term is c. So the constant term in the expanded expression (x + ?)^2 should also be c. Comparing the coefficients, we have:
c = ?^2
Therefore, the values of b and c in the expression x^2 + bx + c = (x + ?)^2 are b = 2? and c = ?^2.