Solve −3x2+30x−27=0−3𝑥2+30𝑥−27=0 for x𝑥 by first taking out a common factor. Enter the smaller number first.
Question
Solve for x
by first taking out a common factor. Enter the smaller number first.
Solution
First, we can factor out a -3 from each term in the equation:
-3(x² - 10x + 9) = 0
Next, we can set the equation inside the parentheses equal to zero (since if a product equals zero, at least one of the factors must be zero):
x² - 10x + 9 = 0
This is a quadratic equation in the form ax² + bx + c = 0. We can solve it by factoring, completing the square, or using the quadratic formula. In this case, the equation factors easily:
(x - 1)(x - 9) = 0
Setting each factor equal to zero gives the solutions x = 1 and x = 9. So, the solutions to the original equation are x = 1 and x = 9. The smaller number is 1.
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