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Create a list of steps, in order, that will solve the following equation.

(x-5)^(2)=25
Solution steps:
Add 5 to both sides
Multiply both sides by 5
Square both sides
Take the square root of both sides

Create a list of steps, in order, that will solve the following equation. $\newline$ $(x-5)^{2}=25$ $\newline$ Solution steps: $\newline$ - Add $5$ to both sides $\newline$ - Multiply both sides by $5$ $\newline$ - Square both sides $\newline$ - Take the square root of both sides

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Solve a quadratic equation using square roots

Full solution

Q. Create a list of steps, in order, that will solve the following equation.

\newline

(x-5)^{2}=25

\newline

Solution steps:

\newline

- Add

5

to both sides

\newline

- Multiply both sides by

5

\newline

- Square both sides

\newline

- Take the square root of both sides

Take square root: Take the square root of both sides of the equation to eliminate the exponent on the left side. $\newline$ $\sqrt{((x-5)^2)} = \sqrt{25}$ $\newline$ This simplifies to $|x - 5| = 5$ , because the square root of a square gives the absolute value of the original expression.
Solve absolute value equation: Solve the resulting absolute value equation. The absolute value equation $|x - 5| = 5$ has two possible solutions: $x - 5 = 5$ or $x - 5 = -5$ .
Solve first equation: Solve the first equation $x - 5 = 5$ . $\newline$ Add $5$ to both sides to isolate $x$ . $\newline$ $x - 5 + 5 = 5 + 5$ $\newline$ $x = 10$
Solve second equation: Solve the second equation $x - 5 = -5$ . $\newline$ Add $5$ to both sides to isolate $x$ . $\newline$ $x - 5 + 5 = -5 + 5$ $\newline$ $x = 0$

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