Solve the equation for all real solutions in simplest form.2, x, squared, minus, 9, x, minus, 2, equals, 02x 2 −9x−2=0
Question
Solve the equation for all real solutions in simplest form.
Solution
To solve the equation 2x^2 - 9x - 2 = 0, we can use the quadratic formula. The quadratic formula states that for an equation of the form ax^2 + bx + c = 0, the solutions for x can be found using the formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
In our equation, a = 2, b = -9, and c = -2. Plugging these values into the quadratic formula, we get:
x = (-(-9) ± √((-9)^2 - 4(2)(-2))) / (2(2))
Simplifying further:
x = (9 ± √(81 + 16)) / 4
x = (9 ± √97) / 4
Therefore, the solutions for x are:
x = (9 + √97) / 4
x = (9 - √97) / 4
These are the real solutions to the equation 2x^2 - 9x - 2 = 0 in simplest form.
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