solve 12t2 + 17t = 40
12t^2 + 17t -40 = 0
Substitute into the quadratic equation to solve.
To solve the equation 12t^2 + 17t = 40, we need to rearrange the equation to set it equal to zero. Let's start by subtracting 40 from both sides:
12t^2 + 17t - 40 = 0
Now, we have a quadratic equation in the form of at^2 + bt + c = 0. To solve this equation, we can use the quadratic formula, which states that for an equation of the form ax^2 + bx + c = 0, the solutions are given by:
x = (-b ± √(b^2 - 4ac)) / (2a)
Applying this formula to our equation 12t^2 + 17t - 40 = 0:
t = (-17 ± √(17^2 - 4(12)(-40))) / (2(12))
Simplifying this equation gives us:
t = (-17 ± √(289 + 1920)) / 24
t = (-17 ± √(2209)) / 24
Taking the square root of 2209 gives us:
t = (-17 ± 47) / 24
So we have two possible values for t:
t1 = (-17 + 47) / 24 = 30 / 24 = 5/4
t2 = (-17 - 47) / 24 = -64 / 24 = -8/3
Therefore, the solutions to the equation 12t^2 + 17t = 40 are t = 5/4 and t = -8/3.