Use factoring to solve each equation:
49t^2=25 How would u do this? Thank You
I would take the square roots of both sides, remembering that there can be either a + or - sign on the square root.
That will leave you with
7 t = + or - 5.
Next, divide both sides by 7.
If you want to use factoring, rewrite the equation as
(7t +5)(7t -5) = 0
You will get the same answer.
How did you get the (7t+5)(7t-5)
From 49t^2 - 25 = 0
(7t+5)(7t-5)= 0 is the factored version of gthe same equation.
Whenever you have the difference of two perfect squares, factoring is easy.
a^2 - b^2 = (a-b)(a+b)
To solve the equation 49t^2 = 25 using factoring, we need to rewrite it in factored form.
Step 1: Begin by subtracting 25 from both sides of the equation to have zero on one side:
49t^2 - 25 = 0
Step 2: Recognize that this equation is in the form of a difference of squares. A difference of squares can be factored into the product of two binomials:
(a^2 - b^2) = (a + b)(a - b)
In this case, a^2 = (7t)^2 and b^2 = 5^2. So we can rewrite the equation as:
(7t)^2 - 5^2 = 0
Step 3: Apply the difference of squares formula to factor the equation:
(7t + 5)(7t - 5) = 0
Now, we have two factors: (7t + 5) and (7t - 5).
Step 4: Set each factor equal to 0 and solve for t:
7t + 5 = 0 or 7t - 5 = 0
For the first factor, subtract 5 from both sides:
7t = -5
Then divide by 7:
t = -5/7
For the second factor, add 5 to both sides:
7t = 5
Then divide by 7:
t = 5/7
So the solutions to the equation 49t^2 = 25 are t = -5/7 and t = 5/7.