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How to factor using quadratic formula 3x2+4x−63x^2+4x-6

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Full solution

Q. How to factor using quadratic formula 3x2+4x−63x^2+4x-6
  1. Identify coefficients: Identify coefficients aa, bb, and cc in the equation 3x2+4x−6=03x^2 + 4x - 6 = 0.\newlinea=3a=3, b=4b=4, c=−6c=-6
  2. Plug into quadratic formula: Plug the coefficients into the quadratic formula: x=−b±b2−4ac2ax = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}.\newlinex=−(4)±(4)2−4⋅(3)⋅(−6)2⋅(3)x = \frac{-(4) \pm \sqrt{(4)^2 - 4\cdot(3)\cdot(-6)}}{2\cdot(3)}
  3. Simplify terms under square root: Simplify the terms under the square root: b2−4acb^2 - 4ac. (4)2−4×(3)×(−6)=16+72=88(4)^2 - 4\times(3)\times(-6) = 16 + 72 = 88
  4. Insert simplified square root: Insert the simplified square root back into the formula. x=−4±886x = \frac{{-4 \pm \sqrt{88}}}{{6}}
  5. Simplify square root of 8888: Simplify the square root of 8888. 88=4×22=2×22\sqrt{88} = \sqrt{4\times22} = 2\times\sqrt{22}
  6. Insert simplified square root: Insert the simplified square root into the formula. x=−4±2226x = \frac{{-4 \pm 2\sqrt{22}}}{{6}}
  7. Simplify equation by dividing: Simplify the equation by dividing all terms by 22.x=−2±223x = \frac{{-2 \pm \sqrt{22}}}{{3}}

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