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Solve the quadratic by factoring.

x^(2)+13 x+36=x+1
Answer:
x=

Solve the quadratic by factoring. $\newline$ $x^{2}+13 x+36=x+1$ $\newline$ Answer: $x=$

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Factor quadratics with leading coefficient 1

Full solution

Q. Solve the quadratic by factoring.

\newline

x^{2}+13 x+36=x+1

\newline

Answer:

x=

Write Equation: Write down the original equation. $\newline$ $x^2 + 13x + 36 = x + 1$
Move Terms: Move all terms to one side of the equation to set it equal to zero. $\newline$ Subtract $x$ and $1$ from both sides to get: $\newline$ $x^2 + 13x + 36 - x - 1 = 0$ $\newline$ Simplify the equation: $\newline$ $x^2 + 12x + 35 = 0$
Simplify Equation: 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 $7$ satisfy these conditions because: $\newline$ $5 \times 7 = 35$ $\newline$ $5 + 7 = 12$ $\newline$ So, the factored form of the equation is: $\newline$ $(x + 5)(x + 7) = 0$
Factor Quadratic: Solve for $x$ by setting each factor equal to zero. $\newline$ $x + 5 = 0$ or $x + 7 = 0$ $\newline$ Solve each equation for $x$ : $\newline$ $x = -5$ or $x = -7$

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