If I solved an equation with the quadratic formula (below)then got my answer (below), how would I answer this correctly and how would I come up with this answer?
2x^2 +3 = 7x
answer:
x = 7 plus or minus 5/ 4
x = ?
2x^2 - 7x + 3 = 0
(2x - 1) (x - 3) = 0
2x - 1 = 0 ... x = 1/2
x - 3 = 0 ... x = 3
The Quadratic Formula says that
x = (7±√(49-24))/(2*2) = (7±√25)/4 = (7±5)/4
To solve the given equation using the quadratic formula, you need to follow these steps:
1. Start by rearranging the equation so that one side is equal to zero:
2x^2 + 3 - 7x = 0
2. The quadratic formula states that for an equation in the form ax^2 + bx + c = 0, the solutions for x are given by:
x = (-b ± √(b^2 - 4ac)) / (2a)
In our equation, a = 2, b = -7, and c = 3. Substitute these values into the quadratic formula:
x = (-(-7) ± √((-7)^2 - 4(2)(3))) / (2(2))
3. Simplify the equation and evaluate:
x = (7 ± √(49 - 24)) / 4
x = (7 ± √25) / 4
x = (7 ± 5) / 4
Now you have two solutions, one with a "+" sign and the other with a "-" sign:
x = (7 + 5) / 4 = 12 / 4 = 3
x = (7 - 5) / 4 = 2 / 4 = 1/2
Therefore, the solutions to the equation 2x^2 + 3 = 7x are x = 3 and x = 1/2.