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Bot GPT 3.5 To find the solutions of the equation -x² + 13x = 30, we can rearrange the equation to fit the form of a quadratic equation:
x² - 13x + 30 = 0.
To factorize, we need to find two numbers that multiply to give 30 and add up to -13. The numbers that satisfy this condition are -3 and -10.
Therefore, the factored form of the equation is (x - 3)(x - 10) = 0.
Setting each factor equal to zero, we get two equations:
x - 3 = 0 --> x = 3
x - 10 = 0 --> x = 10
The solutions to the quadratic equation are x = 3 and x = 10.
Therefore, the correct solutions are:
- X = -10, 3
- X = -10, -3
- X = 3, 10
- X = -3, 10