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Bot GPT 3.5 To solve for x in the equation 0 = 5x^2 + 2x - 12, we need to use the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / 2a
In this case, a = 5, b = 2, and c = -12. Substituting these values into the formula, we get:
x = (-2 ± √(2^2 - 4(5)(-12))) / 2(5)
x = (-2 ± √(4 + 240)) / 10
x = (-2 ± √244) / 10
Now we can simplify by finding the square root of 244:
√244 ≈ 15.62
Substitute this value back into the equation:
x = (-2 ± 15.62) / 10
x = (-2 + 15.62) / 10 or x = (-2 - 15.62) / 10
Solving for each case:
x = 13.62 / 10 or x = -17.62 / 10
Therefore, the solutions for x are:
x = 1.362 or x = -1.762