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$Solve for x. {:[2x^(2)-40 x+200=0],[x=◻]:}$

Solve for $x$ . $\newline$ $\begin{array}{l} 2 x^{2}-40 x+200=0 \\ x=\square \end{array}$

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Solve a quadratic equation by factoring

Full solution

Q. Solve for

x

.

\newline

\begin{array}{l} 2 x^{2}-40 x+200=0 \\ x=\square \end{array}

Identify the quadratic equation: Identify the quadratic equation to be solved. $\newline$ The given quadratic equation is $2x^2 - 40x + 200 = 0$ .
Factor out the greatest common factor: Factor out the greatest common factor (GCF) from the quadratic equation. $\newline$ The GCF of $2x^2$ , $-40x$ , and $200$ is $2$ . Factoring out $2$ gives us: $\newline$ $2(x^2 - 20x + 100) = 0$ .
Divide both sides of the equation: Divide both sides of the equation by the GCF to simplify the equation. $\newline$ Dividing by $2$ , we get: $\newline$ $x^2 - 20x + 100 = 0$ .
Factor the quadratic expression: Factor the quadratic expression. $\newline$ We need to find two numbers that multiply to $100$ and add up to $-20$ . The numbers $-10$ and $-10$ satisfy these conditions. $\newline$ So, we can write the equation as: $\newline$ $(x - 10)(x - 10) = 0$ .
Set each factor equal to zero: Set each factor equal to zero and solve for x. $\newline$ First factor: $x - 10 = 0$ $\newline$ Adding $10$ to both sides gives us $x = 10$ . $\newline$ Second factor: $x - 10 = 0$ $\newline$ This is the same as the first factor, so it gives us the same solution: $x = 10$ .
Write the final solutions for $x$ : Write the final solutions for $x$ . $\newline$ Since both factors give us the same solution, we have a repeated root. The solution for $x$ is $10$ .

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