I need help with this equation, I am really bad at fractions.
m^2 - (49/2 * m)= 1/2
To solve this equation, we need to isolate the variable m. Let's break down the steps:
Step 1: Remove the fraction by multiplying every term in the equation by the common denominator, which in this case is 2.
2 * (m^2) - 2 * (49/2 * m) = 2 * (1/2)
This simplifies to:
2m^2 - 49m = 1
Step 2: Rearrange the equation to get it in standard quadratic form, which is ax^2 + bx + c = 0.
2m^2 - 49m - 1 = 0
Now that we have a quadratic equation, we can solve it using either factoring, completing the square, or the quadratic formula. Let's use the quadratic formula.
Step 3: Apply the quadratic formula, which states that for an equation of the form ax^2 + bx + c = 0, the solutions for x are given by:
x = (-b ± √(b^2 - 4ac)) / 2a
For our equation 2m^2 - 49m - 1 = 0, a = 2, b = -49, and c = -1. Plugging these values into the quadratic formula:
m = (-(-49) ± √((-49)^2 - 4 * 2 * (-1))) / (2 * 2)
Simplifying:
m = (49 ± √(2401 + 8)) / 4
m = (49 ± √(2409)) / 4
Now, you can use a calculator to approximate the value of the square root of 2409 and then substitute it back into the equation to find the values of m.