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The quadratic formula is given by:
x = (-b ± √(b^2 - 4ac)) / (2a),
where a, b, and c are the coefficients of the quadratic equation ax^2 + bx + c = 0.
Here, the coefficients are:
a = 1, b = -7, and c = -6.
Using the quadratic formula:
x = (-(-7) ± √((-7)^2 - 4(1)(-6))) / (2(1))
= (7 ± √(49 + 24)) / 2
= (7 ± √73) / 2
Therefore, the solutions to the equation x^2 – 7x – 6 = 0 are:
x = (7 + √73) / 2
x = (7 - √73) / 2