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$Solve for x. {:[x^(2)-14 x+49=0],[x=]:}$

Solve for $x$ . $\newline$ $\begin{array}{l} x^{2}-14 x+49=0 \\ x=\square \end{array}$

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Solve a quadratic equation by factoring

Full solution

Q. Solve for

x

.

\newline

\begin{array}{l} x^{2}-14 x+49=0 \\ x=\square \end{array}

Identify quadratic equation: Identify the quadratic equation to be solved. $\newline$ The given quadratic equation is $x^2 - 14x + 49 = 0$ .
Find factors of constant term: Look for factors of the constant term ( $49$ ) that add up to the coefficient of the $x$ term ( $-14$ ). $\newline$ The factors of $49$ that add up to $-14$ are $-7$ and $-7$ , since ( $-7$ ) $\times$ ( $-7$ ) = $49$ and ( $-7$ ) $x$ $2$ ( $-7$ ) = $-14$ .
Write factored form of equation: Write the factored form of the quadratic equation using the factors found in Step $2$ . $\newline$ The factored form of the equation is $(x - 7)(x - 7) = 0$ .
Solve for x: Set each factor equal to zero and solve for x. $\newline$ First factor: $x - 7 = 0$ $\newline$ Add $7$ to both sides: $x = 7$ $\newline$ Since both factors are the same, we only need to solve one of them.
Write solution: Write the solution for the equation $x^2 - 14x + 49 = 0$ . $\newline$ The solution is $x = 7$ .

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