Final answer:
The exact values of the number are x = 2 + 3√2 and x = 2 - 3√2.
Step-by-step explanation:
To find the exact value of the number, we can solve the quadratic equation given by x^2 - 4x = 14. Rearranging the equation, we have x^2 - 4x - 14 = 0. Using the quadratic formula, x = (-b ± √(b^2 - 4ac)) / (2a), where a = 1, b = -4, and c = -14. Plugging in these values, we get x = (4 ± √((-4)^2 - 4(1)(-14))) / (2(1)). Simplifying further, we have x = (4 ± √(16 + 56)) / 2, which becomes x = (4 ± √72) / 2. Taking the square root, x = (4 ± 6√2) / 2.
Dividing both numerator and denominator by 2, we get x = 2 ± 3√2. Therefore, the exact values of the number are x = 2 + 3√2 and x = 2 - 3√2.