How do you use the quadratic formula to find both solutions to the quadratic equation #17x^2 = 12x #?

Question

Nathan Axel · Accepted Answer

You don't have to use the quadratic formula.

One solution is in plain view: if #x=0# it holds. If #x!=0# we may divide by #x#: #17x=12->x=12/17=#the other solution.

Eva Adamson · Answer

Using the quadratic formula is, perhaps, not the easiest way to solve this. (I say "perhaps", because easiness is not something someone else can decide for you.)

If you have been told to use the formula. Or if you are curious about how it would work. (After all, we tell students that every quadratic equation can be solved by using the formula.) Then here's how it goes: Solve #17x^2 = 12x# We need to put it in standard form for a quadratic equation: #17x^2 - 12x =0# Now we'll use #x = (-b +- sqrt(b^2-4ac))/(2a)# In this equation, we have: #a=17# #b=-12# #c=0# (That's the one you may have had trouble with on your own.) So we get: #x = (-(-12) +- sqrt((-12)^2-4(17)(0)))/(2(17))# #x = (12 +- sqrt(144-0))/34# # = (12 +- 12)/ 34# So, we have: #x = (12+12)/34 = 24/34 = 12/17# Or #x = (12-12)/34 = 0/34 =0#

Isaiah Anthony · Answer

undefined To use the quadratic formula to find both solutions to the quadratic equation 17x^2 = 12x, follow these steps:

1. Rewrite the equation in standard form: 17x^2 - 12x = 0.
2. Identify the coefficients: a = 17, b = -12, and c = 0.
3. Substitute the values of a, b, and c into the quadratic formula: x = (-b ± √(b^2 - 4ac)) / (2a).
4. Plug in the values: x = (-(-12) ± √((-12)^2 - 4(17)(0))) / (2(17)).
5. Simplify: x = (12 ± √(144 - 0)) / 34.
6. Further simplify: x = (12 ± √144) / 34.
7. Calculate the square root: √144 = 12.
8. Substitute the square root value: x = (12 ± 12) / 34.
9. There are two solutions:
   - Solution 1: x = (12 + 12) / 34 = 24 / 34 = 12 / 17.
   - Solution 2: x = (12 - 12) / 34 = 0 / 34 = 0.

Therefore, the solutions to the quadratic equation 17x^2 = 12x are x = 12/17 and x = 0.