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Solve using the quadratic formula.\newline4m2+8m+3=04m^2 + 8m + 3 = 0\newlineWrite your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.\newlinem=m = _____ or m=m = _____

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Q. Solve using the quadratic formula.\newline4m2+8m+3=04m^2 + 8m + 3 = 0\newlineWrite your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.\newlinem=m = _____ or m=m = _____
  1. Quadratic Formula: The quadratic formula is given by m=−b±b2−4ac2am = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}, where aa, bb, and cc are the coefficients from the quadratic equation am2+bm+c=0am^2 + bm + c = 0. In this case, a=4a = 4, b=8b = 8, and c=3c = 3.
  2. Calculate Discriminant: First, calculate the discriminant, which is the part under the square root in the quadratic formula: b2−4acb^2 - 4ac. Here, it is 82−4(4)(3)8^2 - 4(4)(3).
  3. Perform Calculation: Perform the calculation: 64−48=1664 - 48 = 16.
  4. Apply Discriminant: Now, apply the discriminant to the quadratic formula. Since the discriminant is a perfect square, we will get exact values for mm.
  5. Substitute Values: Substitute the values into the quadratic formula: m=−8±162⋅4m = \frac{{-8 \pm \sqrt{16}}}{{2 \cdot 4}}.
  6. Simplify Square Root: Simplify the square root: 16=4\sqrt{16} = 4.
  7. Split Equation Solutions: Now, split the equation into the two possible solutions for mm using the ±\pm symbol: m=(−8+4)/8m = (-8 + 4) / 8 or m=(−8−4)/8m = (-8 - 4) / 8.
  8. Calculate Each Solution: Calculate each solution: m=(−4)/8m = (-4) / 8 or m=(−12)/8m = (-12) / 8.
  9. Simplify Each Fraction: Simplify each fraction: m=−12m = -\frac{1}{2} or m=−32m = -\frac{3}{2}.

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