Question



Any non-integer answers should be rounded to the nearest tenth.

Solve the equation below.

(x-2)(x-3)=30

Type the solution with the smaller value in the first blank.





Answers

GPT 3.5
To solve the equation (x-2)(x-3)=30, we can first expand the left side of the equation:

x^2 - 5x + 6 = 30

Then, we can subtract 30 from both sides:

x^2 - 5x + 6 - 30 = 0

x^2 - 5x - 24 = 0

To factorize this quadratic equation, we need to find two numbers that multiply to -24 and add to -5. The numbers are -8 and 3:

(x - 8)(x + 3) = 0

Setting each factor equal to zero, we have:

x - 8 = 0 or x + 3 = 0

x = 8 or x = -3

So the solutions to the equation (x-2)(x-3)=30 are x = 8 and x = -3. The smaller value is -3, so the solution is -3.

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