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Use the quadratic formula to solve. Express your answer in simplest form. -2w^(2)+11 w+5=-4w^(2) Answer: w=

Use the quadratic formula to solve. Express your answer in simplest form.\newline−2w2+11w+5=−4w2 -2 w^{2}+11 w+5=-4 w^{2} \newlineAnswer: w= w=

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Composition of linear and quadratic functions: find an equationright chevron icon

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Q. Use the quadratic formula to solve. Express your answer in simplest form.\newline−2w2+11w+5=−4w2 -2 w^{2}+11 w+5=-4 w^{2} \newlineAnswer: w= w=
  1. Simplify the equation: First, we need to simplify the equation by moving all terms to one side to get a standard quadratic equation form ax2+bx+c=0ax^2 + bx + c = 0.−2w2+11w+5=−4w2-2w^2 + 11w + 5 = -4w^2 Add 4w24w^2 to both sides to combine like terms.−2w2+4w2+11w+5=0-2w^2 + 4w^2 + 11w + 5 = 02w2+11w+5=02w^2 + 11w + 5 = 0
  2. Apply quadratic formula: Now that we have the quadratic equation in standard form, we can apply the quadratic formula to find the values of ww. The quadratic formula is given by w=−b±b2−4ac2aw = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}, where aa, bb, and cc are the coefficients from the quadratic equation ax2+bx+c=0ax^2 + bx + c = 0. In our equation, a=2a = 2, b=11b = 11, and c=5c = 5.
  3. Calculate discriminant: Next, we calculate the discriminant b2−4acb^2 - 4ac which is part of the quadratic formula.\newlineDiscriminant = b2−4acb^2 - 4ac\newlineDiscriminant = 112−4(2)(5)11^2 - 4(2)(5)\newlineDiscriminant = 121−40121 - 40\newlineDiscriminant = 8181
  4. Use quadratic formula: Since the discriminant is positive, we will have two real solutions. Now we can use the quadratic formula to find the values of ww.w=−b±Discriminant2aw = \frac{-b \pm \sqrt{\text{Discriminant}}}{2a}w=−11±812×2w = \frac{-11 \pm \sqrt{81}}{2 \times 2}w=−11±94w = \frac{-11 \pm 9}{4}
  5. Solve for w: We will now solve for w using the two possible values for the square root.\newlineFirst solution:\newlinew=(−11+9)/4w = (-11 + 9) / 4\newlinew=−2/4w = -2 / 4\newlinew=−1/2w = -1/2\newlineSecond solution:\newlinew=(−11−9)/4w = (-11 - 9) / 4\newlinew=−20/4w = -20 / 4\newlinew=−5w = -5

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