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Solve using the quadratic formula.\newline8r2+8r+2=08r^2 + 8r + 2 = 0\newlineWrite your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.\newliner=r = _____ or r=r = _____

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Q. Solve using the quadratic formula.\newline8r2+8r+2=08r^2 + 8r + 2 = 0\newlineWrite your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.\newliner=r = _____ or r=r = _____
  1. Identify coefficients: Identify the coefficients of the quadratic equation 8r2+8r+2=08r^2 + 8r + 2 = 0. The standard form of a quadratic equation is ax2+bx+c=0ax^2 + bx + c = 0, where aa, bb, and cc are coefficients. Here, a=8a = 8, b=8b = 8, and c=2c = 2.
  2. Recall quadratic formula: Recall the quadratic formula, which is r=−b±b2−4ac2ar = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}. We will use this formula to find the values of rr.
  3. Substitute coefficients: Substitute the coefficients aa, bb, and cc into the quadratic formula. This gives us r=−(8)±(8)2−4(8)(2)2(8)r = \frac{{-(8) \pm \sqrt{{(8)^2 - 4(8)(2)}}}}{{2(8)}}.
  4. Simplify square root: Simplify the expression inside the square root: (8)2−4(8)(2)=64−64=0(8)^2 - 4(8)(2) = 64 - 64 = 0.
  5. Simplify quadratic formula: Since the discriminant (the value inside the square root) is 00, the square root of 00 is 00. Therefore, the quadratic formula simplifies to r=(−8±0)/16r = (-8 \pm 0) / 16.
  6. Find value of r: Simplify the expression to find the value of r: r=(−8)/16=−12r = (-8) / 16 = -\frac{1}{2}.
  7. Unique solution: Since the discriminant was 00, there is only one unique solution for rr. Therefore, r=−12r = -\frac{1}{2} is the only solution.

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