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Hoochie [10]
4 years ago
10

Solve the following quadratic equation by the square root property of equality. (x - 8)^2 = 48

Mathematics
2 answers:
NeX [460]4 years ago
8 0

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)

mrs_skeptik [129]4 years ago
4 0

Answer:  The required solution of the given equation is

x=8+4\sqrt3,~~8-\sqrt3.

Step-by-step explanation:  We are given to solve the following quadratic equation by the square root property of equality :

(x-8)^2=48~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)

Using the square root property of equality, we have from equation (i) after taking the square roots on both sides that

x-8=\pm\sqrt{48}\\\\\Rightarrow x-8=\pm\sqrt{16\times3}\\\\\Rightarrow x-8=\pm4\sqrt3\\\\\Rightarrow x=8\pm4\sqrt3.

Thus, the required solution of the given equation is

x=8+4\sqrt3,~~8-\sqrt3.

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