2x 2 5x 1 0 complete the square

Asked by maham237 @ 20/02/2021 in Mathematics viewed by 354 People

Solve 5x + 1 = 2x2 + 9x. Which are steps in the process of completing the square used to solve the equation?
ANSWER CHOICES

1 = 2(x2 + 2x)
1 = 2x2 + 4x
2 = 2(x2 + 2x + 1)
3 = 2(x + 1)2
2 = 2(x + 1)2

Answered by maham237 @ 20/02/2021

The first thing we will do for this case is to solve the equation by completing squares.
We have then:
$5x + 1 = 2x ^ 2 + 9x
$
Pass the variables for one side of the equation:
$1 = 2x ^ 2 + 9x - 5x

1 = 2x ^ 2 + 4x$
Common factor 2:
$1 = 2 (x ^ 2 + 2x)
$
Clear the right side:
$1/2 = (x ^ 2 + 2x)
$
Complete squares:
$1/2 + (2/2) ^ 2 = (x ^ 2 + 2x) + (2/2) ^ 2

1/2 + (1) ^ 2 = (x ^ 2 + 2x) + (1) ^ 2

1/2 + 1 = (x ^ 2 + 2x) + 1$
$3/2 = x ^ 2 + 2x + 1

3/2 = (x + 1) ^ 2

3 = 2 (x + 1) ^ 2$
Answer:
Therefore, the steps are:
$1 = 2 (x ^ 2 + 2x)

2 = 2 (x ^ 2 + 2x + 1)

3 = 2 (x + 1) ^ 2$

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