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Varvara68 [4.7K]
3 years ago
6

The expression square root 5x is equivalent to the expression x square root 5

Mathematics
2 answers:
dimulka [17.4K]3 years ago
8 0
\/(5x) = x\/5
[\/(5x]² = [x\/5]²
5x = 5x²
5x²-5x = 0
5x(x-1) = 0
5x = 0 --> x = 0
x-1 = 0 --> x = 1
nexus9112 [7]3 years ago
7 0
√(5x)=x√5
square both sides
5x=5x²
minus 5x both sides
0=5x^2-5x
factor
0=5x(x-1)
set to zero
5x=0
x=0
x-1=0
x=1

x=0 or 1
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Answer:

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Step-by-step explanation:

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Find the roots of the quadratic equation x2 – 8x = 9 by completing the square. Show your work.
omeli [17]

Answer:

The answer is -1 or 9

The quadratic equation is ax² + bx + c  = 0. But, by completing the square we turn it into: a(x + d)² + e = 0, where:

d = b/2a

e = c - b²/4a

Our quadratic equation is x² - 8x = 9, which is after rearrangement:

x² - 8x - 9 = 0

So, a = 1, b = -8, c = -9

Let's first calculate d and e:

d = b/2a = -8/(2 * 1) = -8/2 = -4

e = c - b²/4a = -9 - (-8)²/(4 * 1) = -9 - 64/4 = -9 - 16 = -25

By completing the square we have:

a(x + d)² + e = 0

1(x + (-4))² + (-25) = 0

(x - 4)² - 25 = 0

(x - 4)² = 25

⇒ x - 4 = √25

Since √25 can be either -5  or +5 , then:

x - 4 = -5             or           x - 4 = 5

x = -5 + 4            or           x = 5 + 4

x = -1                   or           x = 9

Step-by-step explanation:

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