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Simplifying 7v2 + -42 = 55v Reorder the terms: -42 + 7v2 = 55v Solving -42 + 7v2 = 55v Solving for variable 'v'. Reorder the terms: -42 + -55v + 7v2 = 55v + -55v Combine like terms: 55v + -55v = 0 -42 + -55v + 7v2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -6 + -7.857142857v + v2 = 0 Move the constant term to the right: Add '6' to each side of the equation. -6 + -7.857142857v + 6 + v2 = 0 + 6 Reorder the terms: -6 + 6 + -7.857142857v + v2 = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -7.857142857v + v2 = 0 + 6 -7.857142857v + v2 = 0 + 6 Combine like terms: 0 + 6 = 6 -7.857142857v + v2 = 6 The v term is -7.857142857v. Take half its coefficient (-3.928571429). Square it (15.43367347) and add it to both sides. Add '15.43367347' to each side of the equation. -7.857142857v + 15.43367347 + v2 = 6 + 15.43367347 Reorder the terms: 15.43367347 + -7.857142857v + v2 = 6 + 15.43367347 Combine like terms: 6 + 15.43367347 = 21.43367347 15.43367347 + -7.857142857v + v2 = 21.43367347 Factor a perfect square on the left side: (v + -3.928571429)(v + -3.928571429) = 21.43367347 Calculate the square root of the right side: 4.62965155 Break this problem into two subproblems by setting (v + -3.928571429) equal to 4.62965155 and -4.62965155.Subproblem 1
v + -3.928571429 = 4.62965155 Simplifying v + -3.928571429 = 4.62965155 Reorder the terms: -3.928571429 + v = 4.62965155 Solving -3.928571429 + v = 4.62965155 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '3.928571429' to each side of the equation. -3.928571429 + 3.928571429 + v = 4.62965155 + 3.928571429 Combine like terms: -3.928571429 + 3.928571429 = 0.000000000 0.000000000 + v = 4.62965155 + 3.928571429 v = 4.62965155 + 3.928571429 Combine like terms: 4.62965155 + 3.928571429 = 8.558222979 v = 8.558222979 Simplifying v = 8.558222979Subproblem 2
v + -3.928571429 = -4.62965155 Simplifying v + -3.928571429 = -4.62965155 Reorder the terms: -3.928571429 + v = -4.62965155 Solving -3.928571429 + v = -4.62965155 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '3.928571429' to each side of the equation. -3.928571429 + 3.928571429 + v = -4.62965155 + 3.928571429 Combine like terms: -3.928571429 + 3.928571429 = 0.000000000 0.000000000 + v = -4.62965155 + 3.928571429 v = -4.62965155 + 3.928571429 Combine like terms: -4.62965155 + 3.928571429 = -0.701080121 v = -0.701080121 Simplifying v = -0.701080121Solution
The solution to the problem is based on the solutions from the subproblems. v = {8.558222979, -0.701080121}
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