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Name the two solutions of 25 = (x – 3)^2

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1 Answer

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Answer: x = 8, x = -2

Explanation:

(x - 3)² = 25

Step 1: Take the square root on each side of the equation.

(x - 3)² = 25

√(x - 3)² = ±√25

Step 2: After taking the square root on each side of the equation, this allows you to solve for x.

x - 3 = ±5

Solution 1

x - 3 = 5

x = 5 + 3

x = 8

Solution 2

x - 3 = - 5

x = -5 + 3

x = -2

Another way to solve this problem is to multiply (x - 3)² using the FOIL methods (first, outer, inner, last) and then set it equal to 25.

(x - 3) (x - 3) = 25

x² - 3x - 3x + 9 = 25

The next step is to add like terms. After adding like terms, solve for x.

x² - 3x - 3x + 9 = 25

x² - 6x + 9 - 25 = 25 - 25

x² - 6x - 16 = 0

Last step is to factor x² - 6x - 16 = 0 so you can solve for the two solutions.

(x - 8) (x + 2) = 0

Solution 1

x - 8 = 0

x = 8

Solution 2

x + 2 = 0

x = -2

User Amrinder Arora
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