Solve x2 - 4x - 7 = 0 by completing the square. what are the solutions?
o 12+ v11,2 - v11)
01-2+ v11.-2 - v11]
012+.15.2+7)

x= 2 + √11 or x = 2 −√11

Step-by-step explanation:

I am going to complete the square step-by-step.

x² − 4x − 7=0

Step 1: Add 7 to both sides.

x² − 4x − 7+ 7 = 0 + 7

x² − 4x = 7

Step 2: The coefficient of -4x is -4. Let b = -4.

Then we need to add (b/2)² = 4 to both sides to complete the square.

Add 4 to both sides.

x² − 4x + 4 = 7 + 4

x² − 4x + 4 = 11

Step 3: Factor left side.

(x−2)² = 11

Step 4: Take square root.

x − 2 = ±√11

Step 5: Add 2 to both sides.

x − 2 + 2 = 2 ±√11

x = 2 ±√11

x= 2 + √11 or x = 2 −√11

-3

step-by-step explanation:

a drawing really does here:

so i draw the horizontal line y=2 and the vertical line x=-2 at this intersection i put b (this is where my right angle is going to be).   so point b is at (-2,2).   point a is 5 units long and is also on y=2 so this point has to be (3,2) or (-7,2) -doesn't matter i will go with (3,2).

now we know c is at (-2,y) we don't know the y yet bet we know that c is on x=-2.

we have the area of the triangle is .5bh=12.5

we know the base length is 5 (ab)

we have the height is (2-y) if you look at your

plug in

.5(5)(2-y)=12.5

solve for y to get the y-coordinate for c

2.5(2-y)=12.5

divide both sides by 2.5 giving:

2-y=5

now subtract 2 on both sides

-y=3

y=-3