To factorize the left hand side of the equation, we need to write the quadratic expression in the form (px + q)(rx + s) where p, q, r, and s are constants.
Given equation:
12x^2 = -2x
To factorize, let's first simplify the equation by dividing both sides by the greatest common factor, which is 2:
6x^2 = -x
Now we can see that the equation already has only one term on both sides. To factorize, we need to write it as a product of two linear factors.
Let's try the two linear factors to be (ax + b)(cx + d):
(6x^2) = (-2x)
(ax + b)(cx + d) = acx^2 + (ad + bc)x + bd
We can see that for the coefficient of x^2, ac must be equal to 6.
Let's try a = 2 and c = 3:
(2x + b)(3x + d) = 6x^2 + (6d + 3b)x + bd
By comparing the coefficients, we can obtain:
6d + 3b = -1 (Coefficient of the x term)
bd = 0 (Constant term)
To satisfy the first equation, one possibility is to let b = 0 and d = -1/6. However, this would make bd = 0, not -1.
Let's try another possibility:
Let b = -1 and d = 1/6:
(2x - 1)(3x + 1/6) = 6x^2 + (3/6 - 2/6)x - 1/6
Simplifying the equation:
(2x - 1)(3x + 1/6) = 6x^2 + (1/6)x - 1/6
Now we can rewrite the quadratic equation in the factored form:
(2x - 1)(3x + 1/6) = 0
So the factored form of the left hand side of the equation is (2x - 1)(3x + 1/6).
Consider the following quadratic equation:
12x^2=−2x
Step 1 of 2 : Using the standard form ax2+bx+c=0
of the given quadratic equation, factor the left hand side of the equation into two linear factors
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