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33 votes
33 votes
Solve the equation by completing the square x^2-3x-18=0

User Maslovsa
by
2.7k points

1 Answer

11 votes
11 votes

Answer:

x = -3, 6

Explanation:

First, add 18 to both sides

x² - 3x - 18 = 0

+ 18 + 18

x² - 3x = 18

Add 9/4 to both sides because that is the square of half of -3

x² - 3x + 9/4 = 18 + 9/4

Multiply both sides by 4 to get rid of the fractions

(x² - 3x + 9/4 = 18 + 9/4)4

4x² - 12x + 9 = 72 + 9 = 81

Factor the left side of the equation

(2x - 3)² = 81

√(2x - 3)² = √81

Because of the square root, this will result in a positive number and a negative number

2x - 3 = 9

2x - 3 = -9

For both equations, add 3 to both sides then divide by 2

2x - 3 = 9

+ 3 +3

2x = 12

2x/2 = 12/2

x = 6

2x - 3 = -9

+ 3 + 3

2x = -6

x = -3

User Yogesh Cl
by
2.7k points
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