Math

Question Solve for ww where w24=0w^{2}-4=0. Write answers as integers or simplified fractions.

Studdy Solution

STEP 1

Assumptions
1. We are given the quadratic equation w24=0 w^{2} - 4 = 0 .
2. We need to solve for the variable w w .
3. The solutions should be expressed as integers or as proper or improper fractions in simplest form.

STEP 2

To solve the quadratic equation w24=0 w^{2} - 4 = 0 , we can factor the left-hand side as a difference of squares.
w24=(w2)(w+2) w^{2} - 4 = (w - 2)(w + 2)

STEP 3

Set each factor equal to zero to find the values of w w .
w2=0orw+2=0 w - 2 = 0 \quad \text{or} \quad w + 2 = 0

STEP 4

Solve the first equation w2=0 w - 2 = 0 for w w .
w=2 w = 2

STEP 5

Solve the second equation w+2=0 w + 2 = 0 for w w .
w=2 w = -2

STEP 6

The solutions to the equation w24=0 w^{2} - 4 = 0 are w=2 w = 2 and w=2 w = -2 .
w=2orw=2 w = 2 \quad \text{or} \quad w = -2
These are the values of w w in simplest form, as required.

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