Question

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

Answer 1

To solve the equation 5x + 1 = 2x^2 + 9x using the method of completing the square, follow these steps: move all terms to one side of the equation, combine like terms, divide all terms by the coefficient of x^2, take half of the coefficient of x, square it, and add it to both sides of the equation, factor the left side of the equation, take the square root of both sides, and solve for x.

Step-by-step explanation:

To solve the equation 5x + 1 = 2x2 + 9x using the method of completing the square, the following steps are used:

1. Move all terms to one side of the equation: 2x2 + 9x - 5x - 1 = 0
2. Combine like terms: 2x2 + 4x - 1 = 0
3. Divide all terms by the coefficient of x2: x2 + 2x - 1/2 = 0
4. Take half of the coefficient of x, square it, and add it to both sides of the equation: x2 + 2x + 1 = 1/4
5. Factor the left side of the equation: (x + 1)2 = 1/4
6. Take the square root of both sides: x + 1 = ±1/2
7. Solve for x: x = -1 ± 1/2

Answer 2

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.