If i'm given the equation
4.23= -.19t^2+2.56t-2.37
how do i find the value of t?
Put the equation into the form
ax^2 + bx + c = 0
then use the quadratic formula to find the solutions.
Rewrite it in standard quadratic form as:
0.19t^2 - 2.56 t +6.60 = 0
The coefficients and constant are:
a = 0.19
b = -2.56
c = 6.6
Then use the quadratic formula for the two roots:
t = [-b +/1 sqrt(b^2-4ac)]/2a
One of the solutions is exactly 10.
The other is 3.4737
To find the value of t in the equation 4.23 = -0.19t^2 + 2.56t - 2.37, you can follow these steps:
Step 1: Rearrange the equation.
- Move the constant term (4.23) to the right side by adding it to both sides:
4.23 + 0.19t^2 - 2.56t + 2.37 = 0
Step 2: Simplify the equation.
- Combine like terms:
0.19t^2 - 2.56t + 6.6 = 0
Step 3: Solve the quadratic equation.
- You now have a quadratic equation in the form of at^2 + bt + c = 0, where a = 0.19, b = -2.56, and c = 6.6.
- To solve the quadratic equation, you can either factor it or use the quadratic formula.
Option 1: Factoring (if possible)
- Attempt to factorize the quadratic equation. However, it may not always be possible for every quadratic equation.
Option 2: Quadratic formula (applicable for any quadratic equation)
- The quadratic formula is given by:
t = (-b ± √(b^2 - 4ac)) / (2a)
- Substitute the values of a, b, and c into the quadratic formula and solve for t.
Step 4: Solve for t.
- Substitute the values of a = 0.19, b = -2.56, and c = 6.6 into the quadratic formula:
t = (-(-2.56) ± √((-2.56)^2 - 4(0.19)(6.6))) / (2(0.19))
t = (2.56 ± √(6.5536 - 4.194)) / 0.38
Step 5: Simplify and calculate.
- Evaluate the square root and carry out the calculations:
t = (2.56 ± √2.3596) / 0.38
t ≈ (2.56 ± 1.536) / 0.38
- Calculate both solutions for t using addition and subtraction:
t ≈ (2.56 + 1.536) / 0.38 or t ≈ (2.56 - 1.536) / 0.38
t ≈ 4.096 / 0.38 or t ≈ 1.024 / 0.38
t ≈ 10.8 or t ≈ 2.694
Therefore, the possible values of t in the equation are approximately t ≈ 10.8 and t ≈ 2.694.