What is the inequality shown
2 answers:
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Answer:
- The two solutions are:
- The next and every step are below.
Explanation:
1. : Given (addition property / add - 3 to both sides)
2. : Given (commom factor - 2)
3.
To obtain the perfect square it was added the square of half of the coefficient of x: (1/2)² = 1/4, inside the parenthesis.
Since, the terms inside the parentthesis are multiplied by - 2, you have to add - 2 (1/4) = - 1/2 to the left side of the equation.
4. Now, you have that the trinomial x² - x + 1/4 is a square perfect trinomial which is factored as (x - 1/2)² and get the expression:
5. Divide both sides by - 2 to get the next expression:
6. The last step is to extract squere root from both sides of the equality: