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$Solve for x. {:[2x^(2)-12 x+18=0],[x=◻]:}$

Solve for $x$ . $\newline$ $\begin{array}{l} 2 x^{2}-12 x+18=0 \\ x=\square \end{array}$

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Solve a quadratic equation by factoring

Full solution

Q. Solve for

x

.

\newline

\begin{array}{l} 2 x^{2}-12 x+18=0 \\ x=\square \end{array}

Step $1$ : Factoring the quadratic equation: We are given the quadratic equation $2x^2 - 12x + 18 = 0$ . To solve for $x$ , we can start by factoring the quadratic or using the quadratic formula. Let's try factoring first.
Step $2$ : Factoring out the greatest common factor: Factor out the greatest common factor (GCF) from the quadratic equation. $\newline$ The GCF of $2x^2$ , $-12x$ , and $18$ is $2$ . So we factor out $2$ from each term. $\newline$ $2(x^2 - 6x + 9) = 0$
Step $3$ : Factoring the quadratic expression: Now we need to factor the quadratic expression $x^2 - 6x + 9$ . $\newline$ We look for two numbers that multiply to $9$ and add up to $-6$ . The numbers $-3$ and $-3$ fit this requirement. $\newline$ $(x - 3)(x - 3) = 0$
Step $4$ : Setting each factor equal to zero: Set each factor equal to zero and solve for $x$ . $\newline$ $x - 3 = 0$ $\newline$ Add $3$ to both sides to solve for $x$ . $\newline$ $x = 3$ $\newline$ Since we have a repeated factor, the solution is a double root.
Step $5$ : Solving for x: Write the final solutions for the equation $2x^2 - 12x + 18 = 0$ . $\newline$ The solutions are $x = 3$ , $x = 3$ , which can be written as a single solution $x = 3$ since it is a repeated root.

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