Solve by completing the square. v^2 − 28v + 17 = 0 Write your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth. v = _____ or v = _____

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Solve by completing the square.  v^2 − 28v + 17 = 0 Write your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.  v = _____ or v = _____

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Set up for completing the square: Write the equation in the form of v^2 + bv = c. The given equation is already in this form: v^2 − 28v + 17 = 0. Subtract 17 from both sides to set the equation up for completing the square. v^2 − 28v = -17Add number to complete square: Find the number to add to both sides to complete the square. To complete the square, we need to add (b/2)^2 to both sides, where b is the coefficient of v. In this case, b = -28, so (b/2)^2 = (-28/2)^2 = (-14)^2 = 196. Add 196 to both sides of the equation. v^2 − 28v + 196 = -17 + 196 v^2 − 28v + 196 = 179Factor left side: Factor the left side of the equation. The left side of the equation is now a perfect square trinomial. (v − 14)^2 = 179Take square root: Take the square root of both sides. To solve for v, take the square root of both sides of the equation. √((v − 14)^2) = ±√179 v − 14 = ±√179Solve for v: Solve for v. Add 14 to both sides of the equation to isolate v. v = 14 ± √179 Since √179 is not a perfect square, we can approximate it to the nearest hundredth. √179 ≈ 13.38 v ≈ 14 ± 13.38Find two values of v: Find the two values of v. v ≈ 14 + 13.38 implies v ≈ 27.38. v ≈ 14 - 13.38 implies v ≈ 0.62. Values of v: 27.38, 0.62

Solve by completing the square. $\newline$ $v^2 - 28v + 17 = 0$ $\newline$ Write your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth. $\newline$ $v =$ _ or $v =$ _

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Solve by completing the square.\newlinev2−28v+17=0v^2 - 28v + 17 = 0v2−28v+17=0\newlineWrite your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.\newlinev=v = v= _____ or v=v = v= _____

Solve by completing the square. $\newline$ $v^2 - 28v + 17 = 0$ $\newline$ Write your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth. $\newline$ $v =$ _ or $v =$ _