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Simplifying 7v2 + -4v + -9 = 0 Reorder the terms: -9 + -4v + 7v2 = 0 Solving -9 + -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'. -1.285714286 + -0.5714285714v + v2 = 0 Move the constant term to the right: Add '1.285714286' to each side of the equation. -1.285714286 + -0.5714285714v + 1.285714286 + v2 = 0 + 1.285714286 Reorder the terms: -1.285714286 + 1.285714286 + -0.5714285714v + v2 = 0 + 1.285714286 Combine like terms: -1.285714286 + 1.285714286 = 0.000000000 0.000000000 + -0.5714285714v + v2 = 0 + 1.285714286 -0.5714285714v + v2 = 0 + 1.285714286 Combine like terms: 0 + 1.285714286 = 1.285714286 -0.5714285714v + v2 = 1.285714286 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 = 1.285714286 + 0.08163265305 Reorder the terms: 0.08163265305 + -0.5714285714v + v2 = 1.285714286 + 0.08163265305 Combine like terms: 1.285714286 + 0.08163265305 = 1.36734693905 0.08163265305 + -0.5714285714v + v2 = 1.36734693905 Factor a perfect square on the left side: (v + -0.2857142857)(v + -0.2857142857) = 1.36734693905 Calculate the square root of the right side: 1.16933611 Break this problem into two subproblems by setting (v + -0.2857142857) equal to 1.16933611 and -1.16933611.Subproblem 1
v + -0.2857142857 = 1.16933611 Simplifying v + -0.2857142857 = 1.16933611 Reorder the terms: -0.2857142857 + v = 1.16933611 Solving -0.2857142857 + v = 1.16933611 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 = 1.16933611 + 0.2857142857 Combine like terms: -0.2857142857 + 0.2857142857 = 0.0000000000 0.0000000000 + v = 1.16933611 + 0.2857142857 v = 1.16933611 + 0.2857142857 Combine like terms: 1.16933611 + 0.2857142857 = 1.4550503957 v = 1.4550503957 Simplifying v = 1.4550503957Subproblem 2
v + -0.2857142857 = -1.16933611 Simplifying v + -0.2857142857 = -1.16933611 Reorder the terms: -0.2857142857 + v = -1.16933611 Solving -0.2857142857 + v = -1.16933611 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 = -1.16933611 + 0.2857142857 Combine like terms: -0.2857142857 + 0.2857142857 = 0.0000000000 0.0000000000 + v = -1.16933611 + 0.2857142857 v = -1.16933611 + 0.2857142857 Combine like terms: -1.16933611 + 0.2857142857 = -0.8836218243 v = -0.8836218243 Simplifying v = -0.8836218243Solution
The solution to the problem is based on the solutions from the subproblems. v = {1.4550503957, -0.8836218243}
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