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Solve using the quadratic formula. 8x2+8x+2=08x^2 + 8x + 2 = 0 Write your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth

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Full solution

Q. Solve using the quadratic formula. 8x2+8x+2=08x^2 + 8x + 2 = 0 Write your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth
  1. Identify coefficients: Identify coefficients for the quadratic formula, where a=8a = 8, b=8b = 8, and c=2c = 2.
  2. Write quadratic formula: Write down the quadratic formula: x=−b±b2−4ac2ax = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}.
  3. Plug in values: Plug in the values of aa, bb, and cc into the quadratic formula: x=−(8)±(8)2−4(8)(2)2(8)x = \frac{{-\left(8\right) \pm \sqrt{{\left(8\right)^2 - 4\left(8\right)\left(2\right)}}}}{{2\left(8\right)}}.
  4. Simplify square root: Simplify inside the square root: x=−8±64−6416x = \frac{{-8 \pm \sqrt{{64 - 64}}}}{16}.
  5. Calculate discriminant: Calculate the discriminant 64−6464 - 64: x=−8±(0)16x = \frac{-8 \pm \sqrt{(0)}}{16}.
  6. Simplify square root: Simplify the square root of the discriminant: x=−8±016x = \frac{{-8 \pm 0}}{{16}}.
  7. Solve for x: Solve for x: x=−816x = -\frac{8}{16}.
  8. Reduce fraction: Reduce the fraction: x=−12x = -\frac{1}{2}.

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