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

the question does not present the options, but this does not interfere with the resolution

Part 1) 

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

could you reply to this with the question so i can ?

7

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