Answer:
[tex]x_1= \frac{\sqrt{{29}}}{2} +\frac{7}{2}\\\\x_2= -\frac{\sqrt{{29}}}{2} +\frac{7}{2}[/tex]
Step-by-step explanation:
1. Subtract 9 from both sides of the equation:
[tex]x^2 - 7x+9-9 = 4-9\\\\x^2 - 7x= -5[/tex]
2. Notice that the coefficient of "x" is 7. Then:
[tex](\frac{7}{2})^2=\frac{49}{4}[/tex]
3. Add [tex]\frac{49}{4}[/tex] to both sides of the equation:
[tex]x^2 - 7x+\frac{49}{4}= \frac{49}{4}-5\\\\x^2 - 7x+\frac{49}{4}= \frac{29}{4}[/tex]
4. Completing the square, you get:
[tex](x -\frac{7}{2})^2= \frac{29}{4}[/tex]
5. To find the solutions, you must square-root both sides of the equation, simplify, and solve for "x". Then, you get:
[tex]\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}[/tex]
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.
