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Solve the quadratic by factoring.

x^(2)-10 x=2x-35
Answer:
x=

Solve the quadratic by factoring. $\newline$ $x^{2}-10 x=2 x-35$ $\newline$ Answer: $x=$

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Factor quadratics with leading coefficient 1

Full solution

Q. Solve the quadratic by factoring.

\newline

x^{2}-10 x=2 x-35

\newline

Answer:

x=

Write Equation: Write down the original equation. $\newline$ $x^2 - 10x = 2x - 35$
Rearrange Terms: Move all terms to one side of the equation to set the equation to zero. $\newline$ $x^2 - 10x - 2x + 35 = 0$ $\newline$ Combine like terms. $\newline$ $x^2 - 12x + 35 = 0$
Combine Like Terms: Factor the quadratic equation. $\newline$ We need to find two numbers that multiply to $35$ and add up to $-12$ . $\newline$ The numbers $-5$ and $-7$ fit this requirement because: $\newline$ $(-5) \times (-7) = 35$ $\newline$ $(-5) + (-7) = -12$ $\newline$ So the factored form is: $\newline$ $(x - 5)(x - 7) = 0$
Factor Quadratic: Solve for $x$ by setting each factor equal to zero. $x - 5 = 0$ or $x - 7 = 0$ Solving each equation gives us: $x = 5$ or $x = 7$

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