Question

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

Answer 1

Answer:

$x_1= \frac{\sqrt{{29}}}{2} +\frac{7}{2}\\\\x_2= -\frac{\sqrt{{29}}}{2} +\frac{7}{2}$

Step-by-step 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:

$(\frac{7}{2})^2=\frac{49}{4}$

3. Add $\frac{49}{4}$ to both sides of the equation:

$x^2 - 7x+\frac{49}{4}= \frac{49}{4}-5\\\\x^2 - 7x+\frac{49}{4}= \frac{29}{4}$

4. Completing the square, you get:

$(x -\frac{7}{2})^2= \frac{29}{4}$

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

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

Answer 2

Answer:

x=7/2+square29/2

Step-by-step explanation:

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