Solve for all values of x by factoring. x^(2)-6x+13=5 Answer: x=

Bring to One Side: Bring all terms to one side of the equation to set it equal to zero. x^2 - 6x + 13 = 5 Subtract 5 from both sides to get: x^2 - 6x + 8 = 0Factor Quadratic Equation: Factor the quadratic equation x^2 - 6x + 8. We need to find two numbers that multiply to 8 (the constant term) and add up to -6 (the coefficient of the x term). The numbers that satisfy these conditions are -4 and -2 because: (-4) * (-2) = 8 (-4) + (-2) = -6 So the factored form is: (x - 4)(x - 2) = 0Solve for x: Solve for x by setting each factor equal to zero. If (x - 4) = 0, then x = 4. If (x - 2) = 0, then x = 2.

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Algebra 1

Factor quadratics with leading coefficient 1

Full solution

Q. Solve for all values of

x

by factoring.

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x^{2}-6 x+13=5

\newline

Answer:

x=

Bring to One Side: Bring all terms to one side of the equation to set it equal to zero. $\newline$ $x^2 - 6x + 13 = 5$ $\newline$ Subtract $5$ from both sides to get: $\newline$ $x^2 - 6x + 8 = 0$
Factor Quadratic Equation: Factor the quadratic equation $x^2 - 6x + 8$ . We need to find two numbers that multiply to $8$ (the constant term) and add up to $-6$ (the coefficient of the $x$ term). The numbers that satisfy these conditions are $-4$ and $-2$ because: $(-4) \times (-2) = 8$ $(-4) + (-2) = -6$ So the factored form is: $(x - 4)(x - 2) = 0$
Solve for x: Solve for x by setting each factor equal to zero. $\newline$ If $(x - 4) = 0$ , then $x = 4$ . $\newline$ If $(x - 2) = 0$ , then $x = 2$ .