b To complete the square, make sure all the variable terms are on one side of the equation and all the constants on the other side.
C
c To complete the square, make sure all the variable terms are on one side of the equation and all the constants on the other side.
D
d To complete the square, make sure all the variable terms are on one side of the equation and all the constants on the other side.
A
a w = - 2 or w=- 26
B
b x = - 1 or x=- 4
C
c k = 17 or k=- 1
D
d z=935 or z=65
Practice makes perfect
a We want to solve the quadratic equation by completing the square. To do so, we will start by rewriting the equation so all terms with w are on one side of the equation and all constants are on the other side.
w^2+28w+52=0
⇕
w^2+28w=- 52In a quadratic expression, b is the linear coefficient. For the equation above, we have that b=28. Let's now calculate ( b2 )^2.
The solutions for this equation are w=- 14 ± 12. Let's separate them into the positive and negative cases.
w=- 14 ± 12
w_1=- 14 + 12
w_2=- 14 - 12
w_1=- 2
w_2=- 26
We found that the solutions of the given equation are w_1=- 2 and w_2=- 26.
b We want to solve the quadratic equation by completing the square. To do so, we will start by rewriting the equation so all terms with x are on one side of the equation and all constants are on the other side.
x^2+5x+4=0
⇕
x^2+5x=- 4In a quadratic expression b is the linear coefficient. For the equation above, we have that b=5. Let's now calculate ( b2 )^2.
The solutions for this equation are x=- 52 ± 32. Let's separate them into the positive and negative cases.
x=- 5/2 ± 3/2
x_1=- 5/2 + 3/2
x_2=- 5/2 - 3/2
x_1=- 2/2
x_2=- 8/2
x_1=- 1
x_2=- 4
We found that the solutions of the given equation are x_1=- 1 and x_2=- 4.
c We want to solve the quadratic equation by completing the square. To do so, we will start by rewriting the equation so all terms with k are on one side of the equation and all constants are on the other side.
k^2-16k-17=0
⇕
k^2-16k=17In a quadratic expression, b is the linear coefficient. For the equation above, we have that b=- 16. Let's now calculate ( b2 )^2.
The solutions for this equation are k=8 ± 9. Let's separate them into the positive and negative cases.
k=8 ± 9
k_1=8 + 9
k_2=8 - 9
k_1=17
k_2=- 1
We found that the solutions of the given equation are k_1=17 and k_2=- 1.
d We want to solve the quadratic equation by completing the square. To do so, we will start by rewriting the equation so all terms with z are on one side of the equation and all constants are on the other side.
z^2-1000z+60 775=0
⇕
z^2-1000z=- 60 775In a quadratic expression, b is the linear coefficient. For the equation above, we have that b=- 1000. Let's now calculate ( b2 )^2.
