solve: 49w^2 - 100
w^2 = 100 / 49
w = 10/7
or
w = -10/7
+-10/7
To solve 49w^2 - 100, we need to find the value(s) of w that make the expression equal to zero. In other words, we are looking for the roots of the expression.
1. Start by setting the expression equal to zero:
49w^2 - 100 = 0
2. Rewrite the equation as a quadratic equation:
(7w)^2 - 10^2 = 0
3. Apply the difference of squares formula:
(7w + 10)(7w - 10) = 0
4. Set each factor equal to zero and solve for w:
7w + 10 = 0 or 7w - 10 = 0
For 7w + 10 = 0:
Subtract 10 from both sides:
7w = -10
Divide both sides by 7:
w = -10/7
For 7w - 10 = 0:
Add 10 to both sides:
7w = 10
Divide both sides by 7:
w = 10/7
So the solutions to 49w^2 - 100 = 0 are w = -10/7 and w = 10/7.