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Simplifying 18v2 + 18v + -5 = 0 Reorder the terms: -5 + 18v + 18v2 = 0 Solving -5 + 18v + 18v2 = 0 Solving for variable 'v'. Begin completing the square. Divide all terms by 18 the coefficient of the squared term: Divide each side by '18'. -0.2777777778 + v + v2 = 0 Move the constant term to the right: Add '0.2777777778' to each side of the equation. -0.2777777778 + v + 0.2777777778 + v2 = 0 + 0.2777777778 Reorder the terms: -0.2777777778 + 0.2777777778 + v + v2 = 0 + 0.2777777778 Combine like terms: -0.2777777778 + 0.2777777778 = 0.0000000000 0.0000000000 + v + v2 = 0 + 0.2777777778 v + v2 = 0 + 0.2777777778 Combine like terms: 0 + 0.2777777778 = 0.2777777778 v + v2 = 0.2777777778 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 = 0.2777777778 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + v2 = 0.2777777778 + 0.25 Combine like terms: 0.2777777778 + 0.25 = 0.5277777778 1.25 + v2 = 0.5277777778 Factor a perfect square on the left side: (v + 0.5)(v + 0.5) = 0.5277777778 Calculate the square root of the right side: 0.726483157 Break this problem into two subproblems by setting (v + 0.5) equal to 0.726483157 and -0.726483157.Subproblem 1
v + 0.5 = 0.726483157 Simplifying v + 0.5 = 0.726483157 Reorder the terms: 0.5 + v = 0.726483157 Solving 0.5 + v = 0.726483157 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 = 0.726483157 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + v = 0.726483157 + -0.5 v = 0.726483157 + -0.5 Combine like terms: 0.726483157 + -0.5 = 0.226483157 v = 0.226483157 Simplifying v = 0.226483157Subproblem 2
v + 0.5 = -0.726483157 Simplifying v + 0.5 = -0.726483157 Reorder the terms: 0.5 + v = -0.726483157 Solving 0.5 + v = -0.726483157 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 = -0.726483157 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + v = -0.726483157 + -0.5 v = -0.726483157 + -0.5 Combine like terms: -0.726483157 + -0.5 = -1.226483157 v = -1.226483157 Simplifying v = -1.226483157Solution
The solution to the problem is based on the solutions from the subproblems. v = {0.226483157, -1.226483157}
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