What is the factor or 12x^2 -78x + 93.5
To determine the factors of the quadratic expression 12x^2 - 78x + 93.5, we can either try factoring it directly or use the quadratic formula.
First, let's try factoring:
Step 1: Multiply the coefficient of the x^2 term (12) with the constant term (93.5).
12 * 93.5 = 1116
Step 2: List all possible pairs of factors of 1116.
Factors of 1116: ±1, ±2, ±3, ±4, ±6, ±12, ±37, ±74, ±111, ±148, ±222, ±333, ±556, ±1116
Step 3: Look for a pair of factors whose sum is equal to the coefficient of the x term (-78).
After trying different pairs, we find that -3 and -74 satisfy this condition since -3 + (-74) = -77.
Step 4: Write the original expression as a product of two binomials using the found factors:
12x^2 - 78x + 93.5 = (4x - 3)(3x - 74)
So, the factored form of 12x^2 - 78x + 93.5 is (4x - 3)(3x - 74).
If factoring did not work, you can always use the quadratic formula:
Given a quadratic equation in the form ax^2 + bx + c = 0, the quadratic formula can be used to find the solutions:
x = (-b ± √(b^2 - 4ac)) / (2a)
For our quadratic expression 12x^2 - 78x + 93.5, the coefficients are:
a = 12, b = -78, c = 93.5
Substituting these values into the quadratic formula, we can solve for x.