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ladessa [460]
3 years ago
9

Show all steps when completing the square to solve 2x^2 - 4x - 5 = 25

Mathematics
1 answer:
aleksley [76]3 years ago
8 0

Answer:

x = 5, -3

Step-by-step explanation:

2x² - 4x - 5 = 25

add 5 to each side

2x² - 4x = 30

factor out the 2

2(x² - 2x) = 30

divide both sides by 2

x² - 2x = 15

divide b by 2, square it -- (b/2)², and add it to both sides

-2/2 = -1 → -1² = 1

x² - 2x + 1 = 15 + 1

factor the expression on the left -- this will be [x - (b/2)]²

(x - 1)² = 16

find the square root of both sides

x - 1 = ±4

add 1 to both sides

x = 4 + 1

x = -4 + 1

solve

x = 5, -3

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Answer: With no choices given here, here are a few possibilities.

If it is not a right triangle, the third side could be any number less than 50 cm

If it is a right triangle, the third side could be the hypotenuse, which would be 10√13 or about 36.05 cm.

If 30cm is the hypotenuse, the other side would be 10√5 or about 22.36 cm

Step-by-step explanation: If the two given sides add up to 50, they flatten out to a straight line, equal to the third side, so it is no longer a triangle. The third side must be less than the sum of the other two sides.

We can use the Pythagorean Theorem a² + b² = c² to calculate the lengths of the sides of a right triangle.

For example

20² + 30² = c²

400 + 900 = c²

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three lines intersect at a point generating 6 angles and one of these angles is 90 degree then the number of other distinct angl
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