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Simplifying 7v2 + -4v = 18 Reorder the terms: -4v + 7v2 = 18 Solving -4v + 7v2 = 18 Solving for variable 'v'. Reorder the terms: -18 + -4v + 7v2 = 18 + -18 Combine like terms: 18 + -18 = 0 -18 + -4v + 7v2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -2.571428571 + -0.5714285714v + v2 = 0 Move the constant term to the right: Add '2.571428571' to each side of the equation. -2.571428571 + -0.5714285714v + 2.571428571 + v2 = 0 + 2.571428571 Reorder the terms: -2.571428571 + 2.571428571 + -0.5714285714v + v2 = 0 + 2.571428571 Combine like terms: -2.571428571 + 2.571428571 = 0.000000000 0.000000000 + -0.5714285714v + v2 = 0 + 2.571428571 -0.5714285714v + v2 = 0 + 2.571428571 Combine like terms: 0 + 2.571428571 = 2.571428571 -0.5714285714v + v2 = 2.571428571 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 = 2.571428571 + 0.08163265305 Reorder the terms: 0.08163265305 + -0.5714285714v + v2 = 2.571428571 + 0.08163265305 Combine like terms: 2.571428571 + 0.08163265305 = 2.65306122405 0.08163265305 + -0.5714285714v + v2 = 2.65306122405 Factor a perfect square on the left side: (v + -0.2857142857)(v + -0.2857142857) = 2.65306122405 Calculate the square root of the right side: 1.628822036 Break this problem into two subproblems by setting (v + -0.2857142857) equal to 1.628822036 and -1.628822036.Subproblem 1
v + -0.2857142857 = 1.628822036 Simplifying v + -0.2857142857 = 1.628822036 Reorder the terms: -0.2857142857 + v = 1.628822036 Solving -0.2857142857 + v = 1.628822036 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 = 1.628822036 + 0.2857142857 Combine like terms: -0.2857142857 + 0.2857142857 = 0.0000000000 0.0000000000 + v = 1.628822036 + 0.2857142857 v = 1.628822036 + 0.2857142857 Combine like terms: 1.628822036 + 0.2857142857 = 1.9145363217 v = 1.9145363217 Simplifying v = 1.9145363217Subproblem 2
v + -0.2857142857 = -1.628822036 Simplifying v + -0.2857142857 = -1.628822036 Reorder the terms: -0.2857142857 + v = -1.628822036 Solving -0.2857142857 + v = -1.628822036 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 = -1.628822036 + 0.2857142857 Combine like terms: -0.2857142857 + 0.2857142857 = 0.0000000000 0.0000000000 + v = -1.628822036 + 0.2857142857 v = -1.628822036 + 0.2857142857 Combine like terms: -1.628822036 + 0.2857142857 = -1.3431077503 v = -1.3431077503 Simplifying v = -1.3431077503Solution
The solution to the problem is based on the solutions from the subproblems. v = {1.9145363217, -1.3431077503}
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