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Solve using the quadratic formula.\newline2w2+4w−5=02w^2 + 4w - 5 = 0\newlineWrite your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.\newlinew=w = _____ or w=w = _____

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Q. Solve using the quadratic formula.\newline2w2+4w−5=02w^2 + 4w - 5 = 0\newlineWrite your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.\newlinew=w = _____ or w=w = _____
  1. Identify coefficients: Identify the coefficients of the quadratic equation.\newlineThe quadratic equation is in the form ax2+bx+c=0ax^2 + bx + c = 0. For the equation 2w2+4w−5=02w^2 + 4w - 5 = 0, the coefficients are:\newlinea = 22\newlineb = 44\newlinec = −5-5
  2. Substitute into formula: Substitute the coefficients into the quadratic formula.\newlineThe quadratic formula is w=−b±b2−4ac2aw = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}. Substituting the values we get:\newlinew=−(4)±(4)2−4(2)(−5)2(2)w = \frac{-(4) \pm \sqrt{(4)^2 - 4(2)(-5)}}{2(2)}
  3. Simplify under square root: Simplify under the square root.\newlineCalculate the discriminant b2−4acb^2 - 4ac:\newlineDiscriminant = (4)2−4(2)(−5)(4)^2 - 4(2)(-5)\newlineDiscriminant = 16+4016 + 40\newlineDiscriminant = 5656
  4. Continue with formula: Continue with the quadratic formula.\newlineNow we have:\newlinew=−4±564w = \frac{-4 \pm \sqrt{56}}{4}
  5. Simplify square root: Simplify the square root. 56\sqrt{56} can be simplified to 4×14\sqrt{4\times14}, which is 2×142\times\sqrt{14}. So now we have: w=−4±2×144w = \frac{-4 \pm 2\times\sqrt{14}}{4}
  6. Divide by 22: Simplify the equation by dividing by 22.\newlineWe can divide the numerator and the denominator by 22 to simplify the expression:\newlinew=−2±142w = \frac{-2 \pm \sqrt{14}}{2}
  7. Write possible solutions: Write the two possible solutions for ww. The two solutions are: w=−2+142w = \frac{-2 + \sqrt{14}}{2} or w=−2−142w = \frac{-2 - \sqrt{14}}{2}
  8. Round to nearest hundredth: Round the values of ww to the nearest hundredth, if required.w≈(−2+3.742)w \approx (\frac{-2 + 3.74}{2}) or w≈(−2−3.742)w \approx (\frac{-2 - 3.74}{2})w≈1.742w \approx \frac{1.74}{2} or w≈−5.742w \approx \frac{-5.74}{2}w≈0.87w \approx 0.87 or w≈−2.87w \approx -2.87

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