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Solve for all values of
a in simplest form.

25=|a+14|
Answer:
a=

Solve for all values of $a$ in simplest form. $\newline$ $25=|a+14|$ $\newline$ Answer: $a=$

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Solve a quadratic equation using square roots

Full solution

Q. Solve for all values of

a

in simplest form.

\newline

25=|a+14|

\newline

Answer:

a=

Understand absolute value equation: Understand the absolute value equation. $\newline$ The equation $25 = |a + 14|$ means that the expression inside the absolute value, $a + 14$ , can be either $25$ or $-25$ , because the absolute value of a number is its distance from zero on the number line, which is always non-negative.
Set up two equations: Set up two separate equations to solve for $a$ . Since the absolute value of $a + 14$ can be either positive or negative $25$ , we write two equations: $1$ ) $a + 14 = 25$ $2$ ) $a + 14 = -25$
Solve first equation for $a$ : Solve the first equation for $a$ . Subtract $14$ from both sides of the equation $a + 14 = 25$ to isolate $a$ . $a + 14 - 14 = 25 - 14$ $a = 11$
Solve second equation for $a$ : Solve the second equation for $a$ . Subtract $14$ from both sides of the equation $a + 14 = -25$ to isolate $a$ . $a + 14 - 14 = -25 - 14$ $a = -39$
Write values of $\newline$ $a$ : Write the values of $\newline$ $a$ . $\newline$ We have found two solutions for the equation $\newline$ $25 = |a + 14|$ , which are $\newline$ $a = 11$ and $\newline$ $a = -39$ .

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