Solve the quadratic by factoring. x^(2)+3x+1=-1 Answer: x=

Set Quadratic Equation Equal: First, we need to set the quadratic equation equal to zero by adding 1 to both sides of the equation. x^2 + 3x + 1 + 1 = -1 + 1 x^2 + 3x + 2 = 0Find Two Numbers: Now, we need to find two numbers that multiply to give the constant term (2) and add to give the coefficient of the x term (3). The numbers that satisfy these conditions are 1 and 2 because: 1 * 2 = 2 1 + 2 = 3Factor Quadratic Equation: We can now factor the quadratic equation using these two numbers. x^2 + 3x + 2 = (x + 1)(x + 2)Find Solutions: To find the solutions, we set each factor equal to zero and solve for x. First factor: x + 1 = 0 x = -1 Second factor: x + 2 = 0 x = -2

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Algebra 1

Factor quadratics with leading coefficient 1

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Q. Solve the quadratic by factoring.

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x^{2}+3 x+1=-1

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Answer:

x=

Set Quadratic Equation Equal: First, we need to set the quadratic equation equal to zero by adding $1$ to both sides of the equation. $\newline$ $x^2 + 3x + 1 + 1 = -1 + 1$ $\newline$ $x^2 + 3x + 2 = 0$
Find Two Numbers: Now, we need to find two numbers that multiply to give the constant term $2$ and add to give the coefficient of the $x$ term $3$ . The numbers that satisfy these conditions are $1$ and $2$ because: $\$1 \times 2 = 2$ $1$ + $2$ = $3$ \)
Factor Quadratic Equation: We can now factor the quadratic equation using these two numbers. $\newline$ $x^2 + 3x + 2 = (x + 1)(x + 2)$
Find Solutions: To find the solutions, we set each factor equal to zero and solve for $x$ . $\newline$ First factor: $x + 1 = 0$ $\newline$ $x = -1$ $\newline$ Second factor: $x + 2 = 0$ $\newline$ $x = -2$