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Simplifying 7v2 = 15 + 6v Solving 7v2 = 15 + 6v Solving for variable 'v'. Reorder the terms: -15 + -6v + 7v2 = 15 + 6v + -15 + -6v Reorder the terms: -15 + -6v + 7v2 = 15 + -15 + 6v + -6v Combine like terms: 15 + -15 = 0 -15 + -6v + 7v2 = 0 + 6v + -6v -15 + -6v + 7v2 = 6v + -6v Combine like terms: 6v + -6v = 0 -15 + -6v + 7v2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -2.142857143 + -0.8571428571v + v2 = 0 Move the constant term to the right: Add '2.142857143' to each side of the equation. -2.142857143 + -0.8571428571v + 2.142857143 + v2 = 0 + 2.142857143 Reorder the terms: -2.142857143 + 2.142857143 + -0.8571428571v + v2 = 0 + 2.142857143 Combine like terms: -2.142857143 + 2.142857143 = 0.000000000 0.000000000 + -0.8571428571v + v2 = 0 + 2.142857143 -0.8571428571v + v2 = 0 + 2.142857143 Combine like terms: 0 + 2.142857143 = 2.142857143 -0.8571428571v + v2 = 2.142857143 The v term is -0.8571428571v. Take half its coefficient (-0.4285714286). Square it (0.1836734694) and add it to both sides. Add '0.1836734694' to each side of the equation. -0.8571428571v + 0.1836734694 + v2 = 2.142857143 + 0.1836734694 Reorder the terms: 0.1836734694 + -0.8571428571v + v2 = 2.142857143 + 0.1836734694 Combine like terms: 2.142857143 + 0.1836734694 = 2.3265306124 0.1836734694 + -0.8571428571v + v2 = 2.3265306124 Factor a perfect square on the left side: (v + -0.4285714286)(v + -0.4285714286) = 2.3265306124 Calculate the square root of the right side: 1.525296893 Break this problem into two subproblems by setting (v + -0.4285714286) equal to 1.525296893 and -1.525296893.Subproblem 1
v + -0.4285714286 = 1.525296893 Simplifying v + -0.4285714286 = 1.525296893 Reorder the terms: -0.4285714286 + v = 1.525296893 Solving -0.4285714286 + v = 1.525296893 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '0.4285714286' to each side of the equation. -0.4285714286 + 0.4285714286 + v = 1.525296893 + 0.4285714286 Combine like terms: -0.4285714286 + 0.4285714286 = 0.0000000000 0.0000000000 + v = 1.525296893 + 0.4285714286 v = 1.525296893 + 0.4285714286 Combine like terms: 1.525296893 + 0.4285714286 = 1.9538683216 v = 1.9538683216 Simplifying v = 1.9538683216Subproblem 2
v + -0.4285714286 = -1.525296893 Simplifying v + -0.4285714286 = -1.525296893 Reorder the terms: -0.4285714286 + v = -1.525296893 Solving -0.4285714286 + v = -1.525296893 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '0.4285714286' to each side of the equation. -0.4285714286 + 0.4285714286 + v = -1.525296893 + 0.4285714286 Combine like terms: -0.4285714286 + 0.4285714286 = 0.0000000000 0.0000000000 + v = -1.525296893 + 0.4285714286 v = -1.525296893 + 0.4285714286 Combine like terms: -1.525296893 + 0.4285714286 = -1.0967254644 v = -1.0967254644 Simplifying v = -1.0967254644Solution
The solution to the problem is based on the solutions from the subproblems. v = {1.9538683216, -1.0967254644}
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