The answer is: " x = 0, 1 " .
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Explanation:
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Given:
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" √(x + 1) − 1 = x " ; Solve for "x" ;

First, let us assume that "x ≥ -1 "

Add "1" to EACH SIDE of the equation:

→ √(x + 1) − 1 + 1 = x + 1 ;

to get:

→ √(x + 1) = x + 1 .

Now, "square" EACH side of the equation:

→ [√(x + 1) ]² = (x + 1 )² ;

to get:

x + 1 = (x + 1)²

↔ (x + 1)² = (x + 1) .

Expand the "left-hand side" of the equation:

→ (x + 1)² = (x + 1)(x +1) ;

Note: (a+b)(c+d) = ac +ad + bc + bd ;

As such: (x + 1)(x + 1) = (x*x) + (x*1) +(1(x) + (1*1) ;
= x² + 1x + 1x + 1 ;
= x² + 2x + 1 ;

Now, substitute this "expanded" value, and bring down the "right-hand side" of the equation; and rewrite the equation:
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" (x + 1)² = (x + 1)(x +1) " ;

→ Rewrite as: " x² + 2x + 1 = x + 1 " ;

Subtract "x" ; and subtract "1" ; from EACH SIDE of the equation:

→ x² + 2x + 1 - x - 1 = x + 1 - x - 1 ;

to get: → x² − x = 0

Factor out an "x" on the "left-hand side" of the equation:
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x² − x = x(x − 1) ;

→ x (x − 1) = 0 ;

We have: "x" and "(x − 1)" ; when either of these two multiplicands are equal to zero, then the "right-hand side of the equation equals "zero" .

So, one value of "x" is "0" .

The other value for "x" ;

→ x − 1 = 0 ;

Add "1" to each side of the equation:

→ x − 1 + 1 = 0 + 1 ;

→ x = 1 ;
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So, the answers:

" x = 0, 1 " .
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4 0

4 years ago

Solve the equation 9z-5-4z= -5

Katyanochek1 [597]

Answer:

z = 0

Step-by-step explanation:

Step 1: Write equation

9z - 5 - 4z = -5

Step 2: Solve for z

Combine like terms: 5z - 5 = -5
Add 5 to both sides: 5z = 0
Divide both sides by 5: z = 0

Step 3: Check

Plug in x to verify it's a solution.

9(0) - 5 - 4(0) = -5

0 - 5 - 0 = -5

-5 = -5

6 0

3 years ago

Read 2 more answers