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.
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.