Solve the quadratic by factoring. 3x^(2)+9x-1=x+2 Answer: x=

Move Terms to One Side: Move all terms to one side of the equation to set it equal to zero. Subtract x and 2 from both sides of the equation. 3x^2 + 9x - 1 - x - 2 = x + 2 - x - 2 This simplifies to: 3x^2 + 8x - 3 = 0Factor Quadratic Equation: Factor the quadratic equation 3x^2 + 8x - 3. We need to find two numbers that multiply to 3 * -3 = -9 and add up to 8. The numbers that satisfy these conditions are 9 and -1. 9 * -1 = -9 9 + (-1) = 8Rewrite Middle Term: Rewrite the middle term using the numbers found in Step 2. 3x^2 + 9x - x - 3 = 0Factor by Grouping: Factor by grouping. Group the first two terms and the last two terms. (3x^2 + 9x) - (x + 3) = 0 Factor out a common factor from each group. 3x(x + 3) - 1(x + 3) = 0Factor Common Binomial: Factor out the common binomial factor. (3x - 1)(x + 3) = 0Set Factors Equal: Set each factor equal to zero and solve for x. 3x - 1 = 0 or x + 3 = 0 For 3x - 1 = 0: 3x = 1 x = 1/3 For x + 3 = 0: x = -3

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Solve the quadratic by factoring.

3x^(2)+9x-1=x+2
Answer:
x=

Solve the quadratic by factoring. $\newline$ $3 x^{2}+9 x-1=x+2$ $\newline$ Answer: $x=$

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Algebra 1

Factor quadratics with other leading coefficients

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Q. Solve the quadratic by factoring.

\newline

3 x^{2}+9 x-1=x+2

\newline

Answer:

x=

Move Terms to One Side: Move all terms to one side of the equation to set it equal to zero. $\newline$ Subtract $x$ and $2$ from both sides of the equation. $\newline$ $3x^2 + 9x - 1 - x - 2 = x + 2 - x - 2$ $\newline$ This simplifies to: $\newline$ $3x^2 + 8x - 3 = 0$
Factor Quadratic Equation: Factor the quadratic equation $3x^2 + 8x - 3$ . We need to find two numbers that multiply to $3 \times -3 = -9$ and add up to $8$ . The numbers that satisfy these conditions are $9$ and $-1$ . $9 \times -1 = -9$ $9 + (-1) = 8$
Rewrite Middle Term: Rewrite the middle term using the numbers found in Step $2$ . $\newline$ $3x^2 + 9x - x - 3 = 0$
Factor by Grouping: Factor by grouping. $\newline$ Group the first two terms and the last two terms. $\newline$ $(3x^2 + 9x) - (x + 3) = 0$ $\newline$ Factor out a common factor from each group. $\newline$ $3x(x + 3) - 1(x + 3) = 0$
Factor Common Binomial: Factor out the common binomial factor. $\newline$ $(3x - 1)(x + 3) = 0$
Set Factors Equal: Set each factor equal to zero and solve for $x$ . $3x - 1 = 0$ or $x + 3 = 0$ For $3x - 1 = 0$ : $3x = 1$ $x = \frac{1}{3}$ For $x + 3 = 0$ : $x = -3$