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

Solve the quadratic by factoring.\newline3x2+9x−1=x+2 3 x^{2}+9 x-1=x+2 \newlineAnswer: x= x=

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Full solution

Q. Solve the quadratic by factoring.\newline3x2+9x−1=x+2 3 x^{2}+9 x-1=x+2 \newlineAnswer: x= x=
  1. Move Terms to One Side: Move all terms to one side of the equation to set it equal to zero.\newlineSubtract xx and 22 from both sides of the equation.\newline3x2+9x−1−x−2=x+2−x−23x^2 + 9x - 1 - x - 2 = x + 2 - x - 2\newlineThis simplifies to:\newline3x2+8x−3=03x^2 + 8x - 3 = 0
  2. Factor Quadratic Equation: Factor the quadratic equation 3x2+8x−33x^2 + 8x - 3. We need to find two numbers that multiply to 3×−3=−93 \times -3 = -9 and add up to 88. The numbers that satisfy these conditions are 99 and −1-1. 9×−1=−99 \times -1 = -9 9+(−1)=89 + (-1) = 8
  3. Rewrite Middle Term: Rewrite the middle term using the numbers found in Step 22.\newline3x2+9x−x−3=03x^2 + 9x - x - 3 = 0
  4. Factor by Grouping: Factor by grouping.\newlineGroup the first two terms and the last two terms.\newline(3x2+9x)−(x+3)=0(3x^2 + 9x) - (x + 3) = 0\newlineFactor out a common factor from each group.\newline3x(x+3)−1(x+3)=03x(x + 3) - 1(x + 3) = 0
  5. Factor Common Binomial: Factor out the common binomial factor.\newline(3x−1)(x+3)=0(3x - 1)(x + 3) = 0
  6. Set Factors Equal: Set each factor equal to zero and solve for xx.3x−1=03x - 1 = 0 or x+3=0x + 3 = 0For 3x−1=03x - 1 = 0:3x=13x = 1x=13x = \frac{1}{3}For x+3=0x + 3 = 0:x=−3x = -3

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