If using the method of completing the square to solve the quadratic equation X^2+4x + 3 = 0, which number would have to be added to "complete the square"?

Write numerical coefficient of y² in the expression 2x² - 15xy – 7y²

Find the center and the radius of the circle with the equation: x^2-2x+y^2+4y+1=0?

Prove (a) cosh2(x) − sinh2(x) = 1 and (b) 1 − tanh 2(x) = sech 2(x). solution (a) cosh2(x) − sinh2(x) = ex + e−x 2 2 − 2 = e2x + 2 + e−2x 4 − = 4 = . (b) we start with the identity proved in part (a): cosh2(x) − sinh2(x) = 1. if we divide both sides by cosh2(x), we get 1 − sinh2(x) cosh2(x) = 1 or 1 − tanh 2(x) = .