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Simplifying 4v2 + 13v + -3 = 0 Reorder the terms: -3 + 13v + 4v2 = 0 Solving -3 + 13v + 4v2 = 0 Solving for variable 'v'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -0.75 + 3.25v + v2 = 0 Move the constant term to the right: Add '0.75' to each side of the equation. -0.75 + 3.25v + 0.75 + v2 = 0 + 0.75 Reorder the terms: -0.75 + 0.75 + 3.25v + v2 = 0 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + 3.25v + v2 = 0 + 0.75 3.25v + v2 = 0 + 0.75 Combine like terms: 0 + 0.75 = 0.75 3.25v + v2 = 0.75 The v term is 3.25v. Take half its coefficient (1.625). Square it (2.640625) and add it to both sides. Add '2.640625' to each side of the equation. 3.25v + 2.640625 + v2 = 0.75 + 2.640625 Reorder the terms: 2.640625 + 3.25v + v2 = 0.75 + 2.640625 Combine like terms: 0.75 + 2.640625 = 3.390625 2.640625 + 3.25v + v2 = 3.390625 Factor a perfect square on the left side: (v + 1.625)(v + 1.625) = 3.390625 Calculate the square root of the right side: 1.841364983 Break this problem into two subproblems by setting (v + 1.625) equal to 1.841364983 and -1.841364983.Subproblem 1
v + 1.625 = 1.841364983 Simplifying v + 1.625 = 1.841364983 Reorder the terms: 1.625 + v = 1.841364983 Solving 1.625 + v = 1.841364983 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-1.625' to each side of the equation. 1.625 + -1.625 + v = 1.841364983 + -1.625 Combine like terms: 1.625 + -1.625 = 0.000 0.000 + v = 1.841364983 + -1.625 v = 1.841364983 + -1.625 Combine like terms: 1.841364983 + -1.625 = 0.216364983 v = 0.216364983 Simplifying v = 0.216364983Subproblem 2
v + 1.625 = -1.841364983 Simplifying v + 1.625 = -1.841364983 Reorder the terms: 1.625 + v = -1.841364983 Solving 1.625 + v = -1.841364983 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-1.625' to each side of the equation. 1.625 + -1.625 + v = -1.841364983 + -1.625 Combine like terms: 1.625 + -1.625 = 0.000 0.000 + v = -1.841364983 + -1.625 v = -1.841364983 + -1.625 Combine like terms: -1.841364983 + -1.625 = -3.466364983 v = -3.466364983 Simplifying v = -3.466364983Solution
The solution to the problem is based on the solutions from the subproblems. v = {0.216364983, -3.466364983}
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