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Simplifying 7v2 + -14v = 178 Reorder the terms: -14v + 7v2 = 178 Solving -14v + 7v2 = 178 Solving for variable 'v'. Reorder the terms: -178 + -14v + 7v2 = 178 + -178 Combine like terms: 178 + -178 = 0 -178 + -14v + 7v2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -25.42857143 + -2v + v2 = 0 Move the constant term to the right: Add '25.42857143' to each side of the equation. -25.42857143 + -2v + 25.42857143 + v2 = 0 + 25.42857143 Reorder the terms: -25.42857143 + 25.42857143 + -2v + v2 = 0 + 25.42857143 Combine like terms: -25.42857143 + 25.42857143 = 0.00000000 0.00000000 + -2v + v2 = 0 + 25.42857143 -2v + v2 = 0 + 25.42857143 Combine like terms: 0 + 25.42857143 = 25.42857143 -2v + v2 = 25.42857143 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 = 25.42857143 + 1 Reorder the terms: 1 + -2v + v2 = 25.42857143 + 1 Combine like terms: 25.42857143 + 1 = 26.42857143 1 + -2v + v2 = 26.42857143 Factor a perfect square on the left side: (v + -1)(v + -1) = 26.42857143 Calculate the square root of the right side: 5.140872633 Break this problem into two subproblems by setting (v + -1) equal to 5.140872633 and -5.140872633.Subproblem 1
v + -1 = 5.140872633 Simplifying v + -1 = 5.140872633 Reorder the terms: -1 + v = 5.140872633 Solving -1 + v = 5.140872633 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 = 5.140872633 + 1 Combine like terms: -1 + 1 = 0 0 + v = 5.140872633 + 1 v = 5.140872633 + 1 Combine like terms: 5.140872633 + 1 = 6.140872633 v = 6.140872633 Simplifying v = 6.140872633Subproblem 2
v + -1 = -5.140872633 Simplifying v + -1 = -5.140872633 Reorder the terms: -1 + v = -5.140872633 Solving -1 + v = -5.140872633 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 = -5.140872633 + 1 Combine like terms: -1 + 1 = 0 0 + v = -5.140872633 + 1 v = -5.140872633 + 1 Combine like terms: -5.140872633 + 1 = -4.140872633 v = -4.140872633 Simplifying v = -4.140872633Solution
The solution to the problem is based on the solutions from the subproblems. v = {6.140872633, -4.140872633}
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