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Simplifying 10v2 + 10v + -21 = 0 Reorder the terms: -21 + 10v + 10v2 = 0 Solving -21 + 10v + 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'. -2.1 + v + v2 = 0 Move the constant term to the right: Add '2.1' to each side of the equation. -2.1 + v + 2.1 + v2 = 0 + 2.1 Reorder the terms: -2.1 + 2.1 + v + v2 = 0 + 2.1 Combine like terms: -2.1 + 2.1 = 0.0 0.0 + v + v2 = 0 + 2.1 v + v2 = 0 + 2.1 Combine like terms: 0 + 2.1 = 2.1 v + v2 = 2.1 The v term is v. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. + 0.25 + v2 = 2.1 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + v2 = 2.1 + 0.25 Combine like terms: 2.1 + 0.25 = 2.35 1.25 + v2 = 2.35 Factor a perfect square on the left side: (v + 0.5)(v + 0.5) = 2.35 Calculate the square root of the right side: 1.532970972 Break this problem into two subproblems by setting (v + 0.5) equal to 1.532970972 and -1.532970972.Subproblem 1
v + 0.5 = 1.532970972 Simplifying v + 0.5 = 1.532970972 Reorder the terms: 0.5 + v = 1.532970972 Solving 0.5 + v = 1.532970972 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + v = 1.532970972 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + v = 1.532970972 + -0.5 v = 1.532970972 + -0.5 Combine like terms: 1.532970972 + -0.5 = 1.032970972 v = 1.032970972 Simplifying v = 1.032970972Subproblem 2
v + 0.5 = -1.532970972 Simplifying v + 0.5 = -1.532970972 Reorder the terms: 0.5 + v = -1.532970972 Solving 0.5 + v = -1.532970972 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + v = -1.532970972 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + v = -1.532970972 + -0.5 v = -1.532970972 + -0.5 Combine like terms: -1.532970972 + -0.5 = -2.032970972 v = -2.032970972 Simplifying v = -2.032970972Solution
The solution to the problem is based on the solutions from the subproblems. v = {1.032970972, -2.032970972}
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