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Simplifying 7v2 + -3v = 8 Reorder the terms: -3v + 7v2 = 8 Solving -3v + 7v2 = 8 Solving for variable 'v'. Reorder the terms: -8 + -3v + 7v2 = 8 + -8 Combine like terms: 8 + -8 = 0 -8 + -3v + 7v2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -1.142857143 + -0.4285714286v + v2 = 0 Move the constant term to the right: Add '1.142857143' to each side of the equation. -1.142857143 + -0.4285714286v + 1.142857143 + v2 = 0 + 1.142857143 Reorder the terms: -1.142857143 + 1.142857143 + -0.4285714286v + v2 = 0 + 1.142857143 Combine like terms: -1.142857143 + 1.142857143 = 0.000000000 0.000000000 + -0.4285714286v + v2 = 0 + 1.142857143 -0.4285714286v + v2 = 0 + 1.142857143 Combine like terms: 0 + 1.142857143 = 1.142857143 -0.4285714286v + v2 = 1.142857143 The v term is -0.4285714286v. Take half its coefficient (-0.2142857143). Square it (0.04591836735) and add it to both sides. Add '0.04591836735' to each side of the equation. -0.4285714286v + 0.04591836735 + v2 = 1.142857143 + 0.04591836735 Reorder the terms: 0.04591836735 + -0.4285714286v + v2 = 1.142857143 + 0.04591836735 Combine like terms: 1.142857143 + 0.04591836735 = 1.18877551035 0.04591836735 + -0.4285714286v + v2 = 1.18877551035 Factor a perfect square on the left side: (v + -0.2142857143)(v + -0.2142857143) = 1.18877551035 Calculate the square root of the right side: 1.090309823 Break this problem into two subproblems by setting (v + -0.2142857143) equal to 1.090309823 and -1.090309823.Subproblem 1
v + -0.2142857143 = 1.090309823 Simplifying v + -0.2142857143 = 1.090309823 Reorder the terms: -0.2142857143 + v = 1.090309823 Solving -0.2142857143 + v = 1.090309823 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '0.2142857143' to each side of the equation. -0.2142857143 + 0.2142857143 + v = 1.090309823 + 0.2142857143 Combine like terms: -0.2142857143 + 0.2142857143 = 0.0000000000 0.0000000000 + v = 1.090309823 + 0.2142857143 v = 1.090309823 + 0.2142857143 Combine like terms: 1.090309823 + 0.2142857143 = 1.3045955373 v = 1.3045955373 Simplifying v = 1.3045955373Subproblem 2
v + -0.2142857143 = -1.090309823 Simplifying v + -0.2142857143 = -1.090309823 Reorder the terms: -0.2142857143 + v = -1.090309823 Solving -0.2142857143 + v = -1.090309823 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '0.2142857143' to each side of the equation. -0.2142857143 + 0.2142857143 + v = -1.090309823 + 0.2142857143 Combine like terms: -0.2142857143 + 0.2142857143 = 0.0000000000 0.0000000000 + v = -1.090309823 + 0.2142857143 v = -1.090309823 + 0.2142857143 Combine like terms: -1.090309823 + 0.2142857143 = -0.8760241087 v = -0.8760241087 Simplifying v = -0.8760241087Solution
The solution to the problem is based on the solutions from the subproblems. v = {1.3045955373, -0.8760241087}
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