Solve for x over the real numbers by completing the square.
(x - 8)² = 48
Take the square root of both sides:
x - 8 = 4 √(3) or x - 8 = -4 √(3)
Add 8 to both sides:
x = 8 + 4 √(3) or x - 8 = -4 √(3)
Add 8 to both sides:
Answer: x = 8 + 4 √(3) or x = 8 - 4 √(3)
Answer: The required solution of the given equation is
[tex]x=8+4\sqrt3,~~8-\sqrt3.[/tex]
Step-by-step explanation: We are given to solve the following quadratic equation by the square root property of equality :
[tex](x-8)^2=48~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]
Using the square root property of equality, we have from equation (i) after taking the square roots on both sides that
[tex]x-8=\pm\sqrt{48}\\\\\Rightarrow x-8=\pm\sqrt{16\times3}\\\\\Rightarrow x-8=\pm4\sqrt3\\\\\Rightarrow x=8\pm4\sqrt3.[/tex]
Thus, the required solution of the given equation is
[tex]x=8+4\sqrt3,~~8-\sqrt3.[/tex]
