7tsquared-4t=3tsquared-1
subtract 3t^2 - 1 from both sides, and you get 4t^2 - 4t + 1 = 0. Then factor. Can you do that?
subtract 3t^2 from each side, add one to each side.
4t^2-4t+1=0
(2t-1)^2=0
take the sqrt for each side, and solve for t.
7t^2 - 4t= 3t^2 - 1
4t^2 -4t +1 = 0
(2t - 1)^2 = 0
2t - 1 = 0
t = 1/2 is the only solution
Thanks!! :]
To solve this equation, we need to simplify the terms and isolate the variable on one side. Let's break it down step by step:
1. Start with the given equation: 7t^2 - 4t = 3t^2 - 1
2. Combine like terms on both sides of the equation. In this case, we combine the terms that have t^2 and t separately.
On the left side: 7t^2 - 3t^2 = 4t^2
On the right side: -4t + t = -3t
The equation now becomes: 4t^2 - 3t = -1
3. Move all terms to one side of the equation, in this case, let's move the -1 to the left side by adding it to both sides:
4t^2 - 3t + 1 = 0
Now our equation is in the form of a quadratic equation (ax^2 + bx + c = 0), where a = 4, b = -3, and c = 1.
4. To solve this quadratic equation, we can either factor it, complete the square, or use the quadratic formula. In this case, factoring is not possible, so we'll use the quadratic formula:
The quadratic formula is given by:
x = (-b ± √(b^2 - 4ac)) / (2a)
Substitute the values of a, b, and c from our equation into the quadratic formula:
t = (-(-3) ± √((-3)^2 - 4 * 4 * 1)) / (2 * 4)
Simplify further:
t = (3 ± √(9 - 16)) / 8
t = (3 ± √(-7)) / 8
Since we have a square root of a negative number, the equation has no real solutions. It means that there are no values of t that satisfy the given equation.
Therefore, the solution to the equation 7t^2 - 4t = 3t^2 - 1 is no real solutions.