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Find a negative value of x that satisfies the equation [(x +...
math SAT SAT-math-test
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Find a negative value of x that satisfies the equation [(x + 1)2 - (2x + 1)]1/2 + 2|x| - 6 = 0

A) -5

B) -4

C) -3

D) -2

E) -1

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judziy
Asked by judziyrep:1.9K
University of Benin Nigeria
22 May 2020

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peter
Peter answeredrep:1.7K
University of Lagos Nigeria
12 August 2020
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[(x + 1)- (2x + 1)]1/2 + 2|x| - 6 = 0

From expansion, 

(x + 1)2 = (x + 1)(x+1)

= x2 + 2x + 1

Substitute this into the initial equation

[x2 + 2x + 1 -(2x + 1)]1/2 + 2|x| - 6 = 0

[x2 + 2x + 1 -2x - 1]1/2 + 2|x| - 6 = 0

[x2]1/2 + 2|x| - 6 = 0

And, x1/2 = √x, Similarly (x2)1/2 = √x2 = x

x + 2|x| = 6

3x = 6

x = 6/3

x = 2

But since we want a negative value

x = -2

Ans D

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