Solve using the quadratic formula. 7v^2 + 2v − 7 = 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 using the quadratic formula.  7v^2 + 2v − 7 = 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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Identify coefficients: Identify the coefficients a, b, and c in the quadratic equation 7v^2 + 2v − 7 = 0. Comparing 7v^2 + 2v − 7 = 0 with the standard form ax^2 + bx + c = 0, we find: a = 7 b = 2 c = -7Substitute values into formula: Substitute the values of a, b, and c into the quadratic formula, v = (-b ± sqrt(b^2 - 4ac)) / (2a). The quadratic formula is v = (-2 ± sqrt(2^2 - 4*7*(-7))) / (2*7).Calculate discriminant: Simplify the expression under the square root, known as the discriminant. Calculate the discriminant: 2^2 - 4*7*(-7) = 4 + 196 = 200.Substitute discriminant into formula: Substitute the discriminant back into the quadratic formula. Now we have v = (-2 ± sqrt(200)) / 14.Simplify square root: Simplify the square root of the discriminant. sqrt(200) can be simplified to 10*sqrt(2) because 200 = 100*2 and sqrt(100) = 10. So, v = (-2 ± 10*sqrt(2)) / 14.Divide by common factor: Simplify the expression by dividing all terms by the common factor if possible. In this case, there is no common factor for all terms, so we proceed with v = (-2 ± 10*sqrt(2)) / 14.Calculate possible solutions: Calculate the two possible solutions for v. First solution: v = (-2 + 10*sqrt(2)) / 14 Second solution: v = (-2 - 10*sqrt(2)) / 14Round values if required: Round the values of v to the nearest hundredth, if required. First solution: v ≈ (-2 + 14.14) / 14 ≈ 12.14 / 14 ≈ 0.87 Second solution: v ≈ (-2 - 14.14) / 14 ≈ -16.14 / 14 ≈ -1.15

Solve using the quadratic formula. $\newline$ $7v^2 + 2v - 7 = 0$ $\newline$ 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 using the quadratic formula.\newline7v2+2v−7=07v^2 + 2v - 7 = 07v2+2v−7=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 using the quadratic formula. $\newline$ $7v^2 + 2v - 7 = 0$ $\newline$ Write your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth. $\newline$ $v =$ _ or $v =$ _