Question

4x^2+12x=3 quadratic formula

Answer 1

To solve the equation 4x^2 + 12x = 3 using the quadratic formula, we can first rewrite the equation in the standard form ax^2 + bx + c = 0.

So, the equation becomes:
4x^2 + 12x - 3 = 0

Now, we can identify the values of a, b, and c:
a = 4
b = 12
c = -3

Next, we can use the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / 2a

Plugging in the values of a, b, and c:
x = (-12 ± √(12^2 - 4*4*-3)) / 2*4
x = (-12 ± √(144 + 48)) / 8
x = (-12 ± √192) / 8

We can simplify further by finding the square root of 192:
x = (-12 ± √(64*3)) / 8
x = (-12 ± 8√3) / 8

Now, we can find the two possible solutions by splitting the equation into two separate solutions:
x1 = (-12 + 8√3) / 8
x2 = (-12 - 8√3) / 8

Therefore, the solutions to the equation 4x^2 + 12x = 3 using the quadratic formula are:
x1 = (-12 + 8√3) / 8
x2 = (-12 - 8√3) / 8