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Simplifying -7v2 + 3 = v Reorder the terms: 3 + -7v2 = v Solving 3 + -7v2 = v Solving for variable 'v'. Reorder the terms: 3 + -1v + -7v2 = v + -1v Combine like terms: v + -1v = 0 3 + -1v + -7v2 = 0 Begin completing the square. Divide all terms by -7 the coefficient of the squared term: Divide each side by '-7'. -0.4285714286 + 0.1428571429v + v2 = 0 Move the constant term to the right: Add '0.4285714286' to each side of the equation. -0.4285714286 + 0.1428571429v + 0.4285714286 + v2 = 0 + 0.4285714286 Reorder the terms: -0.4285714286 + 0.4285714286 + 0.1428571429v + v2 = 0 + 0.4285714286 Combine like terms: -0.4285714286 + 0.4285714286 = 0.0000000000 0.0000000000 + 0.1428571429v + v2 = 0 + 0.4285714286 0.1428571429v + v2 = 0 + 0.4285714286 Combine like terms: 0 + 0.4285714286 = 0.4285714286 0.1428571429v + v2 = 0.4285714286 The v term is 0.1428571429v. Take half its coefficient (0.07142857145). Square it (0.005102040819) and add it to both sides. Add '0.005102040819' to each side of the equation. 0.1428571429v + 0.005102040819 + v2 = 0.4285714286 + 0.005102040819 Reorder the terms: 0.005102040819 + 0.1428571429v + v2 = 0.4285714286 + 0.005102040819 Combine like terms: 0.4285714286 + 0.005102040819 = 0.433673469419 0.005102040819 + 0.1428571429v + v2 = 0.433673469419 Factor a perfect square on the left side: (v + 0.07142857145)(v + 0.07142857145) = 0.433673469419 Calculate the square root of the right side: 0.65853889 Break this problem into two subproblems by setting (v + 0.07142857145) equal to 0.65853889 and -0.65853889.Subproblem 1
v + 0.07142857145 = 0.65853889 Simplifying v + 0.07142857145 = 0.65853889 Reorder the terms: 0.07142857145 + v = 0.65853889 Solving 0.07142857145 + v = 0.65853889 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-0.07142857145' to each side of the equation. 0.07142857145 + -0.07142857145 + v = 0.65853889 + -0.07142857145 Combine like terms: 0.07142857145 + -0.07142857145 = 0.00000000000 0.00000000000 + v = 0.65853889 + -0.07142857145 v = 0.65853889 + -0.07142857145 Combine like terms: 0.65853889 + -0.07142857145 = 0.58711031855 v = 0.58711031855 Simplifying v = 0.58711031855Subproblem 2
v + 0.07142857145 = -0.65853889 Simplifying v + 0.07142857145 = -0.65853889 Reorder the terms: 0.07142857145 + v = -0.65853889 Solving 0.07142857145 + v = -0.65853889 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-0.07142857145' to each side of the equation. 0.07142857145 + -0.07142857145 + v = -0.65853889 + -0.07142857145 Combine like terms: 0.07142857145 + -0.07142857145 = 0.00000000000 0.00000000000 + v = -0.65853889 + -0.07142857145 v = -0.65853889 + -0.07142857145 Combine like terms: -0.65853889 + -0.07142857145 = -0.72996746145 v = -0.72996746145 Simplifying v = -0.72996746145Solution
The solution to the problem is based on the solutions from the subproblems. v = {0.58711031855, -0.72996746145}
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