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Simplifying 10v2 + 25v + -11 = 0 Reorder the terms: -11 + 25v + 10v2 = 0 Solving -11 + 25v + 10v2 = 0 Solving for variable 'v'. Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -1.1 + 2.5v + v2 = 0 Move the constant term to the right: Add '1.1' to each side of the equation. -1.1 + 2.5v + 1.1 + v2 = 0 + 1.1 Reorder the terms: -1.1 + 1.1 + 2.5v + v2 = 0 + 1.1 Combine like terms: -1.1 + 1.1 = 0.0 0.0 + 2.5v + v2 = 0 + 1.1 2.5v + v2 = 0 + 1.1 Combine like terms: 0 + 1.1 = 1.1 2.5v + v2 = 1.1 The v term is 2.5v. Take half its coefficient (1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. 2.5v + 1.5625 + v2 = 1.1 + 1.5625 Reorder the terms: 1.5625 + 2.5v + v2 = 1.1 + 1.5625 Combine like terms: 1.1 + 1.5625 = 2.6625 1.5625 + 2.5v + v2 = 2.6625 Factor a perfect square on the left side: (v + 1.25)(v + 1.25) = 2.6625 Calculate the square root of the right side: 1.631716887 Break this problem into two subproblems by setting (v + 1.25) equal to 1.631716887 and -1.631716887.Subproblem 1
v + 1.25 = 1.631716887 Simplifying v + 1.25 = 1.631716887 Reorder the terms: 1.25 + v = 1.631716887 Solving 1.25 + v = 1.631716887 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + v = 1.631716887 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + v = 1.631716887 + -1.25 v = 1.631716887 + -1.25 Combine like terms: 1.631716887 + -1.25 = 0.381716887 v = 0.381716887 Simplifying v = 0.381716887Subproblem 2
v + 1.25 = -1.631716887 Simplifying v + 1.25 = -1.631716887 Reorder the terms: 1.25 + v = -1.631716887 Solving 1.25 + v = -1.631716887 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + v = -1.631716887 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + v = -1.631716887 + -1.25 v = -1.631716887 + -1.25 Combine like terms: -1.631716887 + -1.25 = -2.881716887 v = -2.881716887 Simplifying v = -2.881716887Solution
The solution to the problem is based on the solutions from the subproblems. v = {0.381716887, -2.881716887}
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