the question does not present the options, but this does not interfere with the resolution
Part 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 (+/-)[a-4.5]=2.5
(+)[a-4.5]=2.5> a=7
(-)[a-4.5]=2.5> a=2
the answer part 1) a=7 and a=2
Part 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 (+/-)[a+4.5]=2.5
(+)[a+4.5]=2.5> a=-2
(-)[a+4.5]=2.5> a=-7
the answer part 2) a=-7 and a=-2
Part 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 (+/-)[a+1.5]=3.5
(+)[a+1.5]=3.5> a=2
(-)[a+1.5]=3.5> a=-5
the answer part 3) a=2 and a=-5
Part 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 (+/-)[a+2.5]=4.5
(+)[a+2.5]=4.5> a=2
(-)[a+2.5]=4.5> a=-7
the answer part 4) a=2 and a=-7
Part 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 =20.25
(+/-)[a-2.5]=√20.25 (+/-)[a-2.5]=4.5
(+)[a-2.5]=4.5> a=7
(-)[a-2.5]=4.5> a=-2
the answer part 5) a=7 and a=-2
