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Find all real solutions using the Quaar x²-4x-24=0

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Final answer:

The real solutions to the quadratic equation x²-4x-24=0 are obtained using the quadratic formula, resulting in x = 2 + √7 and x = 2 - √7.

Step-by-step explanation:

To find all real solutions to the quadratic equation x²-4x-24=0, we can use the quadratic formula. This formula is applicable to any equation of the form ax²+bx+c=0. The quadratic formula is expressed as x = (-b ± √(b²-4ac))/(2a).

For the given equation, a=1, b=-4, and c=-24. Plugging these values into the quadratic formula, we get:

x = (4 ± √((4)²-4(1)(-24)))/(2(1))
x = (4 ± √(16+96))/(2)
x = (4 ± √(112))/(2)
x = (4 ± √(4√7))/(2)
x = (4 ± 2√7)/(2)
x = 2 ± √7

Thus, the real solutions to the equation are x = 2 + √7 and x = 2 - √7.

User Ishan Fernando
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