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Simplifying 7v2 + -14v + -49 = -10 Reorder the terms: -49 + -14v + 7v2 = -10 Solving -49 + -14v + 7v2 = -10 Solving for variable 'v'. Reorder the terms: -49 + 10 + -14v + 7v2 = -10 + 10 Combine like terms: -49 + 10 = -39 -39 + -14v + 7v2 = -10 + 10 Combine like terms: -10 + 10 = 0 -39 + -14v + 7v2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -5.571428571 + -2v + v2 = 0 Move the constant term to the right: Add '5.571428571' to each side of the equation. -5.571428571 + -2v + 5.571428571 + v2 = 0 + 5.571428571 Reorder the terms: -5.571428571 + 5.571428571 + -2v + v2 = 0 + 5.571428571 Combine like terms: -5.571428571 + 5.571428571 = 0.000000000 0.000000000 + -2v + v2 = 0 + 5.571428571 -2v + v2 = 0 + 5.571428571 Combine like terms: 0 + 5.571428571 = 5.571428571 -2v + v2 = 5.571428571 The v term is -2v. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2v + 1 + v2 = 5.571428571 + 1 Reorder the terms: 1 + -2v + v2 = 5.571428571 + 1 Combine like terms: 5.571428571 + 1 = 6.571428571 1 + -2v + v2 = 6.571428571 Factor a perfect square on the left side: (v + -1)(v + -1) = 6.571428571 Calculate the square root of the right side: 2.563479778 Break this problem into two subproblems by setting (v + -1) equal to 2.563479778 and -2.563479778.Subproblem 1
v + -1 = 2.563479778 Simplifying v + -1 = 2.563479778 Reorder the terms: -1 + v = 2.563479778 Solving -1 + v = 2.563479778 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + v = 2.563479778 + 1 Combine like terms: -1 + 1 = 0 0 + v = 2.563479778 + 1 v = 2.563479778 + 1 Combine like terms: 2.563479778 + 1 = 3.563479778 v = 3.563479778 Simplifying v = 3.563479778Subproblem 2
v + -1 = -2.563479778 Simplifying v + -1 = -2.563479778 Reorder the terms: -1 + v = -2.563479778 Solving -1 + v = -2.563479778 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + v = -2.563479778 + 1 Combine like terms: -1 + 1 = 0 0 + v = -2.563479778 + 1 v = -2.563479778 + 1 Combine like terms: -2.563479778 + 1 = -1.563479778 v = -1.563479778 Simplifying v = -1.563479778Solution
The solution to the problem is based on the solutions from the subproblems. v = {3.563479778, -1.563479778}
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