What are the approximate solutions of 4x2 + 3 = −12x to the nearest hundredth?

Given the quadratic function:

4x^2 + 3 = - 12x

Can be written as,

4x^2 +12x + 3

a = 4

b = 12

c= 3

Find the zeros or the solution:

Solution:
In order to solve for the roots or zeros of an equation, we simply must look at the 2nd and 3rd value. First we must think of two numbers that when added, the answer is 12, and when multiplied, the answer is 3. Hence, if we are unable to find the number, we will use the quadratic formula.

The Quadratic formula:

x = −b ± √(b^2 − 4ac)/2a

is used to solve quadratic equations where a ≠ 0, in the form
ax^2+bx+c=0

When b^2−4ac=0 there is one real root.

When b^2−4ac>0 there are two real roots.

When b^2−4ac<0 there are no real roots, only a complex number.

Substitute the given values of a, b and c to the quadratic formula.

x = −b ± √(b^2 − 4ac)/2a

x = −(12) ± √((12)^2 − 4(4)(3))/2(4)

x = -12 ± √(144 − 48)/8

x = -12 ± √(96)/8

x = -12 ± 9.8/8

Solve for +- separately.

x = -12 + 9.8/8
x = -0.275

x = -12 - 9.8 /8
x = -2.725

Final answer:

x = -0.275

x = -2.725