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6x^(2)+7x+1=0

6x2+7x+1=0 6 x^{2}+7 x+1=0

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Full solution

Q. 6x2+7x+1=0 6 x^{2}+7 x+1=0
  1. Identify Coefficients: Identify the coefficients of the quadratic equation.\newlineIn the equation 6x2+7x+1=06x^2 + 7x + 1 = 0, the coefficients are a=6a = 6, b=7b = 7, and c=1c = 1.
  2. Apply Quadratic Formula: Apply the quadratic formula, x=−b±b2−4ac2ax = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}.\newlineHere, b2−4ac=72−4⋅6⋅1=49−24=25b^2 - 4ac = 7^2 - 4\cdot6\cdot1 = 49 - 24 = 25.
  3. Calculate Discriminant: Calculate the discriminant b2−4ac\sqrt{b^2 - 4ac}.25=5\sqrt{25} = 5.
  4. Solve for x: Solve for x using the positive and negative values of the square root.\newlinex=−7+52⋅6=−212=−16x = \frac{-7 + 5}{2\cdot6} = \frac{-2}{12} = -\frac{1}{6},\newlinex=−7−52⋅6=−1212=−1x = \frac{-7 - 5}{2\cdot6} = \frac{-12}{12} = -1.

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