what is the answer to 12x^2-18x-21
the only thing I can see is to take out a common factor of 3
12x^2-18x-21
= 3(4x^2 - 6x - 7)
the trinomial does not factor
To find the answer to the expression 12x^2 - 18x - 21, we need to simplify or factorize the expression, if possible.
Step 1: Check if there is a common factor among the terms.
In this case, there is no common factor among 12x^2, -18x, and -21.
Step 2: Determine if the quadratic expression can be factored.
To do this, we check if the quadratic expression can be written in the form (ax + b)(cx + d) or (ax - b)(cx - d) where a, b, c, and d are integers.
If it can be factored, we can then find the roots of the expression by setting each factor equal to zero and solving for x.
However, after inspecting the expression 12x^2 - 18x - 21, we can see that it cannot be factored easily using simple integer values for a, b, c, and d.
Step 3: Use the quadratic formula.
Since the expression cannot be factored easily, we can instead use the quadratic formula to find the roots.
The quadratic formula states that for a quadratic equation in the form ax^2 + bx + c = 0, the roots (or solutions) are given by:
x = (-b ± √(b^2 - 4ac)) / (2a)
By comparing our expression to the quadratic equation form, we can assign values to a, b, and c accordingly:
a = 12, b = -18, c = -21
Plugging these values into the quadratic formula, we get:
x = (-(-18) ± √((-18)^2 - 4 * 12 * (-21))) / (2 * 12)
Simplifying:
x = (18 ± √(324 + 1008)) / 24
x = (18 ± √1332) / 24
x = (18 ± 36.55) / 24
This leads to two possible solutions:
x = (18 + 36.55) / 24
x = 54.55 / 24
x ≈ 2.27
x = (18 - 36.55) / 24
x = -18.55 / 24
x ≈ -0.77
So the possible solutions to the expression 12x^2 - 18x - 21 are x ≈ 2.27 and x ≈ -0.77.