Solve x 2 - 4x - 7 = 0 by completing the square. What are the solutions? {2 + , 2 - } {-2 + , -2 - } {2 + , 2 + }

Question

asked Dec 9, 2021 148k views

1 Answer

Jaywayco · Answer 1 · 2021-12-13T20:39:54+0000

Explanation:

x^(2) - 4x - 7 = 0

First, let's move the
to the right-hand side so we can determine what constant we'll need on the left-hand side to complete the square:

x^(2) - 4x = 7

From here, since the coefficient of the
term is
, we know the square will be
(x - 2) (since
it's half of
).

To complete this square, we will need to add
(-2)^(2) to both sides of the equation:

x^(2) - 4x + (-2)^2 = 7 + ^(-2)

x^(2) - 4x + 4 = 7 + 4

(x - 2)^(2) = 11

Now we can take the square root of both sides to figure out the solutions to
:

$x - 2 = \pm √(11)$

$x = 2 \pm √(11)$