To solve the equation -7x^2 - 10 = -12x, we need to bring all the terms to one side and set the equation equal to zero:
-7x^2 - 12x - 10 = 0
To solve this quadratic equation, we can use the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
In our equation, a = -7, b = -12, and c = -10. Plugging in these values, we get:
x = (-(-12) ± √((-12)^2 - 4(-7)(-10))) / (2(-7))
x = (12 ± √(144 - 280)) / (-14)
x = (12 ± √(-136)) / (-14)
The expression inside the square root, -136, is negative. This means the quadratic equation has no real solutions.
Instead, we can write our solutions using imaginary numbers. The square root of -136 can be written as √(136)i, where i is the imaginary unit (√-1).
So our solutions are:
x = (12 ± √(136)i) / (-14)
Alternatively, we can simplify the expression:
x = (6 ± 2√34i) / (-7)
Therefore, the conjugate pair solutions are:
(6 + 2√34i) / (-7) and (6 - 2√34i) / (-7)
Solve the equation -7x^2 - 10 = -12x. Write your conjugate pair solution(s) as two values separated by a ± sign.
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