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Solve $(x-5)^2 = 4$

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Polynomial vocabulary

Full solution

Q. Solve

(x-5)^2 = 4

Understand the problem: Understand the problem. $\newline$ We need to find the value of $x$ that satisfies the equation $(x-5)^2 = 4$ . This is a quadratic equation in the form of a square of a binomial set equal to a constant.
Take square root: Take the square root of both sides of the equation. $\newline$ To solve for $x$ , we need to eliminate the square on the left side. We do this by taking the square root of both sides of the equation, which gives us two possible solutions: $x - 5 = 2$ or $x - 5 = -2$ .
Solve for x $x=7$ : Solve for x when $x - 5 = 2$ . Adding $5$ to both sides of the equation $x - 5 = 2$ gives us $x = 2 + 5$ , which simplifies to $x = 7$ .
Solve for x $x=3$ : Solve for x when $x - 5 = -2$ . $\newline$ Adding $5$ to both sides of the equation $x - 5 = -2$ gives us $x = -2 + 5$ , which simplifies to $x = 3$ .

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