Question

(60 points)

Please answer and explain all 3 questions, thank you!

2. What number must be added to both sides of the equation to complete the square?

x^2-16x=-8
A. 16
B. -64
C. -16
D. 64

5. Solve
2x^2 + x -1=2

A. No real solutions
B. (1,-3/2)
C. x= -1+3/2
D. (-1,2)


6. Solve.

2x^2 - 4x=0

A.(-6,-2)
B.(0,1/2)
C. (0,2)
D.(0,-2)

Answer 1

2. D. 64

5. B. 1, -3/2

6. C. 0, 2

Explanation:

`2.\\(a-b)^2=a^2-2ab+b^2\\\\x^2-16x=-8\\\\x^2-2(x)(8)=-8\\\\\text{We have}\ 2ab=2(x)(8).\ \text{Therefore}\ b=8.\\\\x^2-2(x)(8)=-8\qquad\text{add}\ 8^2=64\ \text{to both sides}\\\\x^2-2(x)(8)+8^2=-8+64\\\\(x-8)^2=56`

`5.\\2x^2+x-1=2\qquad\text{subtract 2 from both sides}\\\\2x^2+x-3=0\\\\2x^2+3x-2x-3=0\\\\x(2x+3)-1(2x+3)=0\\\\(2x+3)(x-1)=0\iff 2x+3=0\ \vee\ x-1=0\\\\2x+3=0\qquad\text{subtract 3 from both sides}\\2x=-3\qquad\text{divide both sides by 2}\\\boxed{x=-(3)/(2)}\\\\x-1=0\qquad\text{add 1 to both sides}\\\boxed{x=1}`

`6.\\2x^2-4x=0\qquad\text{divide both sides by 2}\\\\x^2-2x=0\\\\x(x-2)=0\iff x=0\ \vee\ x-2=0\\\\\boxed{x=0}\\\\x-2=0\qquad\text{add 2 to both sides}\\\boxed{x=2}`