what are the values of x in the equation (2x+2)^2=4

Question

algebra 1

Answer 1

(2x + 2)² = 4 ←Take the square root of both sides to get:

2x + 2 = ±√4

2x + 2 = ±2 ←This is both +2 or -2 because (+2)² = 4 and (-2)² = 4

Case 1:

Consider the right side as "+2" to get

2x + 2 = 2 ←subtract 2 from both sides to get:

2x = 0 ←Divide both sides by 2 to get:

x = 0

Case 2:

Consider the right side as "-2" to get

2x + 2 = -2 ←subtract 2 from both sides to get:

2x = -4 ←Divide both sides by 2 to get:

x = -2

So there are two answers: x = 0 and x = -2

Answer 2

Answer 3

Answer 4

What are the values of (x) that satisfy the equation (2x + 2)^2 =4

Step 1:

First of all, evaluate the equation and take the square root of both sides.

The square root of (2x + 2)^2 = square root of ( 2x + 2)^2 = + - (square root of 4)

Simplify (2x + 2) = + - (2)

Step 2:

Solve for x:

2x + 2 = 2 subtract 2 from both sides = 2x = 2 - 2

Simplify: 2x = 0

Isolate (x) by dividing 2 from both sides

x = 0/2 (x = 0)

Step 3:

Solving for ( x ) when the equation is 2x + 2 = - 2

Subtract 2 from both sides: 2x = - 2 - 2

Simplify: 2x = - 4

2x= -4 Isolate (x) by dividing 2 from both sides

x = - 4 divided by 2

Simplify: x = -2

Solution:

The values of x that satisfy the equation are 0 and - 2

x = 0 and x = - 2

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Answer 5

You can take the square root of both sides:

√(2x+2)^2 = ±√4

Then you have two solutions:

2x+2 = +2 and 2x+2 = -2

Now, you can subtract from both sides -2:

2x = +2 - 2 and 2x = -2 - 2

2x = 0 and 2x = - 4

Dividing both sides by 2 on the two solutions:

x = 0 and x = - 2

Answer 6

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Answer 7

You could also use FOIL to multiply the left side to give 4x² + 8x + 4 = 4

Subtract 4 from both sides: 4x² + 8x = 0

Divide by 4: x² + 2x = 0

Factor out the x: x(x + 2) = 0

so x = 0, or x + 2 = 0 and x = -2

Check by substituting the two values into the original equation.

Answer 8

First, take the square root of both sides (Positive AND Negative values): (2x + 2) = +2 AND (2x + 2) = -2.

Second, solve each equation:

Case 1 (Positive) Case 2 (Negative)

2x + 2 = 2 2x+2 = -2

2x = 2 - 2 2x = -2 - 2 = -4

2x = 0 x = -4/2

Answers:

x = 0 x = -2