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Simplifying 7v2 + -4v + -2 = 0 Reorder the terms: -2 + -4v + 7v2 = 0 Solving -2 + -4v + 7v2 = 0 Solving for variable 'v'. Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -0.2857142857 + -0.5714285714v + v2 = 0 Move the constant term to the right: Add '0.2857142857' to each side of the equation. -0.2857142857 + -0.5714285714v + 0.2857142857 + v2 = 0 + 0.2857142857 Reorder the terms: -0.2857142857 + 0.2857142857 + -0.5714285714v + v2 = 0 + 0.2857142857 Combine like terms: -0.2857142857 + 0.2857142857 = 0.0000000000 0.0000000000 + -0.5714285714v + v2 = 0 + 0.2857142857 -0.5714285714v + v2 = 0 + 0.2857142857 Combine like terms: 0 + 0.2857142857 = 0.2857142857 -0.5714285714v + v2 = 0.2857142857 The v term is -0.5714285714v. Take half its coefficient (-0.2857142857). Square it (0.08163265305) and add it to both sides. Add '0.08163265305' to each side of the equation. -0.5714285714v + 0.08163265305 + v2 = 0.2857142857 + 0.08163265305 Reorder the terms: 0.08163265305 + -0.5714285714v + v2 = 0.2857142857 + 0.08163265305 Combine like terms: 0.2857142857 + 0.08163265305 = 0.36734693875 0.08163265305 + -0.5714285714v + v2 = 0.36734693875 Factor a perfect square on the left side: (v + -0.2857142857)(v + -0.2857142857) = 0.36734693875 Calculate the square root of the right side: 0.606091527 Break this problem into two subproblems by setting (v + -0.2857142857) equal to 0.606091527 and -0.606091527.Subproblem 1
v + -0.2857142857 = 0.606091527 Simplifying v + -0.2857142857 = 0.606091527 Reorder the terms: -0.2857142857 + v = 0.606091527 Solving -0.2857142857 + v = 0.606091527 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '0.2857142857' to each side of the equation. -0.2857142857 + 0.2857142857 + v = 0.606091527 + 0.2857142857 Combine like terms: -0.2857142857 + 0.2857142857 = 0.0000000000 0.0000000000 + v = 0.606091527 + 0.2857142857 v = 0.606091527 + 0.2857142857 Combine like terms: 0.606091527 + 0.2857142857 = 0.8918058127 v = 0.8918058127 Simplifying v = 0.8918058127Subproblem 2
v + -0.2857142857 = -0.606091527 Simplifying v + -0.2857142857 = -0.606091527 Reorder the terms: -0.2857142857 + v = -0.606091527 Solving -0.2857142857 + v = -0.606091527 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '0.2857142857' to each side of the equation. -0.2857142857 + 0.2857142857 + v = -0.606091527 + 0.2857142857 Combine like terms: -0.2857142857 + 0.2857142857 = 0.0000000000 0.0000000000 + v = -0.606091527 + 0.2857142857 v = -0.606091527 + 0.2857142857 Combine like terms: -0.606091527 + 0.2857142857 = -0.3203772413 v = -0.3203772413 Simplifying v = -0.3203772413Solution
The solution to the problem is based on the solutions from the subproblems. v = {0.8918058127, -0.3203772413}
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