we have that
N 1)
a²
− 9a + 14 = 0
Group terms that contain the same variable, and move the
constant to the opposite side of the equation
(a² − 9a)=-14
Complete
the square Remember to balance the equation by adding the same constants
to each side
(a² − 9a+20.25)=-14+20.25
Rewrite as perfect squares
(a-4.5)²=6.25--------> (a-4.5)=(+/-)√6.25
a1=4.5+√6.25-----> a1=7
a2=4.5-√6.25-----> a2=2
the solution problem N 1 is the pair {7, 2}
N 2)
a²
+ 9a + 14 = 0
Group terms that contain the same variable, and move the constant to the opposite side of the equation
(a² + 9a)=-14
Complete the square Remember to balance the equation by adding the same constants to each side
(a² +9a+20.25)=-14+20.25
Rewrite as perfect squares
(a+4.5)²=6.25--------> (a+4.5)=(+/-)√6.25
a1=-4.5+√6.25-----> a1=-2
a2=-4.5-√6.25-----> a2=-7
the solution problem N 2 is the pair {-2,-7}
N 3)
a² + 3a − 10 = 0
Group terms that contain the same variable, and move the constant to the opposite side of the equation
(a² + 3a)=10
Complete the square Remember to balance the equation by adding the same constants to each side
(a² + 3a+2.25)=10+2.25
Rewrite as perfect squares
(a+1.5)²=12.25------> (a+1.5)=(+/-)√12.25
a1=-1.5+√12.25-----> a1=2
a2=-1.5-√12.25-----> a2=-5
the solution problem N 3 is the pair {2, -5}
N 4)
a²
+ 5a − 14 = 0
Group terms that contain the same variable, and move the constant to the opposite side of the equation
(a² + 5a) =14
Complete the square Remember to balance the equation by adding the same constants to each side
(a² + 5a+6.25) =14+6.25
Rewrite as perfect squares
(a+2.5)² =20.25-------> (a+2.5)=(+/-)√20.25
a1=-2.5+√20.25-----> a1=2
a2=-2.5-√20.25-----> a2=-7
the solution problem N 4 is the pair {2, -7}
N 5)
a² − 5a − 14 = 0
Group terms that contain the same variable, and move the constant to the opposite side of the equation
(a² − 5a)=14
Complete the square Remember to balance the equation by adding the same constants to each side
(a² − 5a+6.25)=14+6.25
Rewrite as perfect squares
(a-2.5)²=2025--------> (a-2.5)=(+/-)√20.25
a1=2.5+√20.25-----> a1=7
a2=2.5-√20.25-----> a2=-2
the solution problem N 5 is the pair {7, -2}
