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 pairs {-2, 7} {2, -7} {-2, -7} {7, 2}

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) 

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) 

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)

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) 

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}

594 square inches

step-by-step explanation:

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