How do you solve #x^2 - 5x = 36#?
Subtract 36 from both sides
This is the equation of a quadratic so wee need the x-intercepts.
Two numbers that multiply to 36 are 4 and -9, and they add to -5 so your equation can be
minus 36 (both sides)
Now, we need to find two numbers (for exampe a and b).
So, the solution is:
We want these brackets to be equal to zero.
The first step is to set the stated expression equal to zero. we will do this by subtracting 36 from both sides:
Now, we can either factor this equation OR use The Quadratic Formula to find the values of
Based on the order of the equation (second order due to the presence of
Now, we just need to figure out what two numbers satisfy the following system:
We know that 36 is a square, so a possible combination is 6 and -6. However, that would not satisfy the first equation. Other factors of -36 include:
The only set there that would satisfy the first equation though, is
We have our two solutions for
Using The Quadratic Formula:
We plug in our equations coefficients into the formula: