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Use the quadratic formula to solve. Express your answer in simplest form. 8w^(2)-27 w+25=3w Answer: w=

Use the quadratic formula to solve. Express your answer in simplest form.\newline8w2−27w+25=3w 8 w^{2}-27 w+25=3 w \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.\newline8w2−27w+25=3w 8 w^{2}-27 w+25=3 w \newlineAnswer: w= w=
  1. Bring to Standard Form: First, we need to bring the equation to standard quadratic form, which is ax2+bx+c=0ax^2 + bx + c = 0. \newline8w2−27w+25=3w8w^2 - 27w + 25 = 3w\newlineSubtract 3w3w from both sides to get:\newline8w2−27w+25−3w=08w^2 - 27w + 25 - 3w = 0\newline8w2−30w+25=08w^2 - 30w + 25 = 0
  2. Apply Quadratic Formula: Now that we have the quadratic equation in standard form, we can apply the quadratic formula to find the solutions for ww. The quadratic formula is given by:\newlinew=−b±b2−4ac2aw = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\newlinewhere a=8a = 8, b=−30b = -30, and c=25c = 25.
  3. Calculate Discriminant: Next, we calculate the discriminant, which is the part under the square root in the quadratic formula: b2−4acb^2 - 4ac.\newlineDiscriminant = (−30)2−4(8)(25)(-30)^2 - 4(8)(25)\newlineDiscriminant = 900−800900 - 800\newlineDiscriminant = 100100
  4. Find Solutions: Since the discriminant is positive, we will have two real solutions. Now we can plug the values of aa, bb, and cc into the quadratic formula to find the solutions for ww. \newlinew=−(−30)±1002×8w = \frac{-(-30) \pm \sqrt{100}}{2 \times 8}\newlinew=30±1016w = \frac{30 \pm 10}{16}
  5. Solve for w: We will now solve for ww using the two possible values for the ±\pm sign.\newlineFirst solution:\newlinew=30+1016w = \frac{30 + 10}{16}\newlinew=4016w = \frac{40}{16}\newlinew=2.5w = 2.5\newlineSecond solution:\newlinew=30−1016w = \frac{30 - 10}{16}\newlinew=2016w = \frac{20}{16}\newlinew=1.25w = 1.25

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