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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

Respuesta :

carlosego
The first thing we will do for this case is to solve the equation by completing squares.
 We have then:
 [tex]5x + 1 = 2x ^ 2 + 9x [/tex]
 Pass the variables for one side of the equation:
 [tex]1 = 2x ^ 2 + 9x - 5x 1 = 2x ^ 2 + 4x[/tex]
 Common factor 2:
 [tex]1 = 2 (x ^ 2 + 2x) [/tex]
 Clear the right side:
 [tex]1/2 = (x ^ 2 + 2x) [/tex]
 Complete squares:
 [tex]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[/tex]
 [tex]3/2 = x ^ 2 + 2x + 1 3/2 = (x + 1) ^ 2 3 = 2 (x + 1) ^ 2[/tex]
 Answer:
 Therefore, the steps are:
 [tex]1 = 2 (x ^ 2 + 2x) 2 = 2 (x ^ 2 + 2x + 1) 3 = 2 (x + 1) ^ 2[/tex]

Answer:

Choices (1), (2) and (4)

Step-by-step explanation:

5x + 1 = 2x² + 9x

By subtracting 5x form both the sides of the equation.

(5x + 1) - 5x = 2x² + 9x - 5x

1 = 2x² + 4x

1 = 2(x² + 2x)

By adding 2 on both the sides

1 + 2 = 2(x² + 2x) + 2

1 + 2 = 2(x² + 2x + 1)

3 = 2(x² + 2x + 1)

3 = 2(x + 1)²

Therefore, choices (1), (2) and (4) are the steps that have been used to complete the square.

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