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$Solve for x. {:[2x^(2)-28 x+98=0],[x=◻]:}$

Solve for $x$ . $\newline$ $\begin{array}{l} 2 x^{2}-28 x+98=0 \\ x=\square \end{array}$

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Solve a quadratic equation by factoring

Full solution

Q. Solve for

x

.

\newline

\begin{array}{l} 2 x^{2}-28 x+98=0 \\ x=\square \end{array}

Identify the quadratic equation: Identify the quadratic equation to solve. $\newline$ The given quadratic equation is $2x^2 - 28x + 98 = 0$ .
Factor out the greatest common factor: Factor out the greatest common factor (GCF) if possible. $\newline$ The GCF of the coefficients $2$ , $-28$ , and $98$ is $2$ . Let's factor it out. $\newline$ $2(x^2 - 14x + 49) = 0$
Factor the quadratic expression: Factor the quadratic expression inside the parentheses. $\newline$ We need to find two numbers that multiply to $49$ and add up to $-14$ . The numbers $-7$ and $-7$ fit this requirement. $\newline$ $2(x - 7)(x - 7) = 0$
Set each factor equal to zero: Set each factor equal to zero and solve for $x$ . $\newline$ Since we have a repeated factor, we only need to set it to zero once. $\newline$ $x - 7 = 0$ $\newline$ Add $7$ to both sides to solve for $x$ . $\newline$ $x = 7$

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