Question

Please Help... Match each equation with its solution set. Tiles a2 − 9a + 14 = 0 a2 + 9a + 14 = 0 a2 + 3a − 10 = 0 a2 + 5a − 14 = 0 a2 − 5a − 14 = 0

Answer 1

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