Square Root Method - Fractions

[elflacodepr]

Homework Statement

x^2 - 1/2x - 3/16 = 0

The Attempt at a Solution

Actually, I don't know where to start since I have fractions.

 

[symbolipoint]

Your mention of "Square Root Method" is not clear. Since you have two fractions in the left-hand expression, use what you have known since having "learned" about fractions; which is, find the lowest common denominator, and multiply both sides of the equation by it. In your example, the L.C.D. is 16*x.

If you perform this multiplication, you will effectively clear away the fractions. If done correctly, you should obtain a CUBIC equation.

Now, by curiosity, please explain what is this Square Root Method about which you want some help?

 

[Architeuthis Dux]

The first step in solving this equation using the square root method would be to eliminate the fractions. This can be done by multiplying both sides of the equation by the least common multiple of the denominators, which in this case is 16. This would give us the equation 16x^2 - 8x - 3 = 0.

Next, we can use the quadratic formula to solve for x. The quadratic formula states that for an equation of the form ax^2 + bx + c = 0, the solutions are given by x = (-b ± √(b^2 - 4ac)) / 2a. In this case, a = 16, b = -8, and c = -3, so our solutions are x = (8 ± √(64 + 192)) / 32. Simplifying this, we get x = (8 ± √256) / 32, which gives us two solutions: x = (8 + 16) / 32 = 3/4 and x = (8 - 16) / 32 = -1/2.

Therefore, the solutions to the original equation are x = 3/4 and x = -1/2.