Complete the square for 5x^2-30x=5

Mathematics

2 answers:

xxMikexx [17]3 years ago

8 0

Answer: (x-3)^2=10

Step-by-step explanation:

Nikitich [7]3 years ago

3 0

Solve for x over the real numbers: by completing the square:

5 x^2 - 30 x = 5

Divide both sides by 5:

x^2 - 6 x = 1

Add 9 to both sides:

x^2 - 6 x + 9 = 10

Write the left hand side as a square:

(x - 3)^2 = 10

Take the square root of both sides:

x - 3 = sqrt(10) or x - 3 = -sqrt(10)

Add 3 to both sides:

x = 3 + sqrt(10) or x - 3 = -sqrt(10)

Add 3 to both sides:

Answer: | x = 3 + sqrt(10) or x = 3 - sqrt(10)

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dezoksy [38]

Domain is the entire span left to right (on the x-axis) that the graph is on. Since the graph goes from x=-4 and ends at x=4, the domain would be from -4 to 4. The circle at -4 is open, so it does not include the point at -4, just everything leading up to it. So, the domain would be

$- 4 < x \leqslant 4$

The range is similar, it is the entire span that the graph goes up and down (on the y-axis). The graph starts at the bottom at y=-2, and ends at y=5. The bottom point (4,-2) is closed, so the graph includes that point, and the top point (-4,5) is open and doesn't include the point. Therefore, the range would be

$- 2 \leqslant x < 5$