Question

Complete the square leave your answer in root form. 2x² - 6x - 3 = 0

Answer 1

x = 1.5 ± √3.75

Explanation:

There are several variations of completing the sqaure.

This is the one I use.

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2x² - 6x - 3 = 0

add 3 to both sides

2x² - 6x = 3

the x² coefficient must be 1

so divide both sides by 2

x² - 3x = 1.5

use half the x coefficient (-3/2 = -1.5) as the complete the square term

(x - 1.5)² = 1.5 + (-1.5)²

(x - 1.5)² = 1.5 + 2.25

(x - 1.5)² = 3.75

Take the square root of both sides

x - 1.5 = ± √3.75

add 1.5 to both sides

x = 1.5 ± √3.75

Answer 2

x = 1.5 + √3.75 ; x = 1.5 - √3.75

Explanation:

2x² - 6x -3 = 0

Add 3 to both sides

2x² - 6x = 3

Divide the entire equation by the coefficient of x²

`(2x^(2))/(2)-(6x)/(2)=(3)/(2)\\`

x² - 3x = 1.5

Divide the coefficient of x by 2 and then square it and add to both sides.

3/2 = 1.5

1.5² = 2.25

Add 2.25 to both sides

x² - 3x + 2.25 = 1.5+2.25

(x - 1.5)² = 3.75

Take square root,

x - 1.5 = ±√3.75

x = 1.5 ± √3.75