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Solve using the quadratic formula.\newline8f2+4f−1=08f^2 + 4f - 1 = 0\newlineWrite your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.\newlinef=f = _____ or f=f = _____

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Q. Solve using the quadratic formula.\newline8f2+4f−1=08f^2 + 4f - 1 = 0\newlineWrite your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.\newlinef=f = _____ or f=f = _____
  1. Identify coefficients: Identify the coefficients aa, bb, and cc in the quadratic equation 8f2+4f−1=08f^2 + 4f - 1 = 0 by comparing it to the standard form ax2+bx+c=0ax^2 + bx + c = 0.\newlinea=8a = 8\newlineb=4b = 4\newlinec=−1c = -1
  2. Substitute values into formula: Substitute the values of aa, bb, and cc into the quadratic formula f=−b±b2−4ac2af = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}.f=−(4)±(4)2−4⋅(8)⋅(−1)2⋅(8)f = \frac{-(4) \pm \sqrt{(4)^2 - 4\cdot(8)\cdot(-1)}}{2\cdot(8)}
  3. Simplify discriminant: Simplify the expression under the square root (the discriminant). (4)2−4⋅(8)⋅(−1)=16+32=48\sqrt{(4)^2 - 4\cdot(8)\cdot(-1)} = \sqrt{16 + 32} = \sqrt{48}
  4. Simplify square root: Further simplify the square root of 4848 to its simplest radical form.\newline48=16×3=4×3\sqrt{48} = \sqrt{16 \times 3} = 4 \times \sqrt{3}
  5. Substitute simplified value: Now, substitute the simplified square root back into the quadratic formula.\newlinef=(−(4)±4⋅3)/(2⋅(8))f = (-(4) \pm 4 \cdot \sqrt{3}) / (2\cdot(8))\newlinef=(−4±4⋅3)/16f = (-4 \pm 4 \cdot \sqrt{3}) / 16
  6. Divide by denominator: Simplify the expression by dividing both terms in the numerator by the denominator.\newlinef=(−14±(14)⋅3)f = \left(-\frac{1}{4} \pm \left(\frac{1}{4}\right) \cdot \sqrt{3}\right)
  7. Find two solutions: Now, we have two possible solutions for ff.f=−14+(14)⋅3f = -\frac{1}{4} + \left(\frac{1}{4}\right) \cdot \sqrt{3} or f=−14−(14)⋅3f = -\frac{1}{4} - \left(\frac{1}{4}\right) \cdot \sqrt{3}
  8. Round to nearest hundredth: If necessary, round the values of ff to the nearest hundredth.f≈−0.25+0.25×1.73f \approx -0.25 + 0.25 \times 1.73 or f≈−0.25−0.25×1.73f \approx -0.25 - 0.25 \times 1.73f≈−0.25+0.4325f \approx -0.25 + 0.4325 or f≈−0.25−0.4325f \approx -0.25 - 0.4325f≈0.1825f \approx 0.1825 or f≈−0.6825f \approx -0.6825f≈0.18f \approx 0.18 or f≈−0.68f \approx -0.68

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