Question

After completing the square, what are the solutions to the quadratic equation

below?
x^2 - 7x+9 = 4​

Answer 1

x=7/2+square29/2

Explanation:

I’m guessing this is right using the top answer because the test doesn’t have the answer flipped like that.

Answer 2

`x_1= \frac{\sqrt{{29}}}{2} +(7)/(2)\\\\x_2= -\frac{\sqrt{{29}}}{2} +(7)/(2)`

Explanation:

1. Subtract 9 from both sides of the equation:

`x^2 - 7x+9-9 = 4-9\\\\x^2 - 7x= -5`

2. Notice that the coefficient of "x" is 7. Then:

`((7)/(2))^2=(49)/(4)`

3. Add
`(49)/(4)` to both sides of the equation:

`x^2 - 7x+(49)/(4)= (49)/(4)-5\\\\x^2 - 7x+(49)/(4)= (29)/(4)`

4. Completing the square, you get:

`(x -(7)/(2))^2= (29)/(4)`

5. To find the solutions, you must square-root both sides of the equation, simplify, and solve for "x". Then, you get:

`\sqrt{(x -(7)/(2))^2}= \±\sqrt{(29)/(4)}\\\\x -(7)/(2)=\±\frac{\sqrt{{29}}}{2} \\\\x= \±\frac{\sqrt{{29}}}{2} +(7)/(2)\\\\\\x_1= \frac{\sqrt{{29}}}{2} +(7)/(2)\\\\x_2= -\frac{\sqrt{{29}}}{2} +(7)/(2)`