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Solve using the quadratic formula.\newlineu2+5u3=0u^2 + 5u - 3 = 0\newlineWrite your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.\newlineu=u = _____ or u=u = _____

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Q. Solve using the quadratic formula.\newlineu2+5u3=0u^2 + 5u - 3 = 0\newlineWrite your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.\newlineu=u = _____ or u=u = _____
  1. Quadratic Formula: The quadratic formula is given by u=b±b24ac2au = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}, where aa, bb, and cc are the coefficients from the quadratic equation au2+bu+c=0au^2 + bu + c = 0. In our case, a=1a = 1, b=5b = 5, and c=3c = -3.
  2. Calculate Discriminant: First, we calculate the discriminant, which is the part under the square root in the quadratic formula: b24acb^2 - 4ac. So we have 524(1)(3)=25+12=375^2 - 4(1)(-3) = 25 + 12 = 37.
  3. Apply Quadratic Formula: Now we can apply the quadratic formula with our values for aa, bb, and cc. We have u=5±372×1u = \frac{-5 \pm \sqrt{37}}{2 \times 1}.
  4. Calculate Solutions: We will have two solutions, one for the addition and one for the subtraction. Let's calculate them separately.\newlineFor the addition: u=5+372u = \frac{-5 + \sqrt{37}}{2}.\newlineFor the subtraction: u=5372u = \frac{-5 - \sqrt{37}}{2}.
  5. Express Solutions as Decimals: The solutions are not integers or proper fractions, and we cannot simplify 37\sqrt{37} any further. So we will express the solutions as decimals rounded to the nearest hundredth.\newlineFor the addition: u(5+6.08)/21.08/20.54u \approx (-5 + 6.08) / 2 \approx 1.08 / 2 \approx 0.54.\newlineFor the subtraction: u(56.08)/211.08/25.54u \approx (-5 - 6.08) / 2 \approx -11.08 / 2 \approx -5.54.

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