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Simplifying 5v2 + -44v + -24 = 0 Reorder the terms: -24 + -44v + 5v2 = 0 Solving -24 + -44v + 5v2 = 0 Solving for variable 'v'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -4.8 + -8.8v + v2 = 0 Move the constant term to the right: Add '4.8' to each side of the equation. -4.8 + -8.8v + 4.8 + v2 = 0 + 4.8 Reorder the terms: -4.8 + 4.8 + -8.8v + v2 = 0 + 4.8 Combine like terms: -4.8 + 4.8 = 0.0 0.0 + -8.8v + v2 = 0 + 4.8 -8.8v + v2 = 0 + 4.8 Combine like terms: 0 + 4.8 = 4.8 -8.8v + v2 = 4.8 The v term is -8.8v. Take half its coefficient (-4.4). Square it (19.36) and add it to both sides. Add '19.36' to each side of the equation. -8.8v + 19.36 + v2 = 4.8 + 19.36 Reorder the terms: 19.36 + -8.8v + v2 = 4.8 + 19.36 Combine like terms: 4.8 + 19.36 = 24.16 19.36 + -8.8v + v2 = 24.16 Factor a perfect square on the left side: (v + -4.4)(v + -4.4) = 24.16 Calculate the square root of the right side: 4.915282291 Break this problem into two subproblems by setting (v + -4.4) equal to 4.915282291 and -4.915282291.Subproblem 1
v + -4.4 = 4.915282291 Simplifying v + -4.4 = 4.915282291 Reorder the terms: -4.4 + v = 4.915282291 Solving -4.4 + v = 4.915282291 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '4.4' to each side of the equation. -4.4 + 4.4 + v = 4.915282291 + 4.4 Combine like terms: -4.4 + 4.4 = 0.0 0.0 + v = 4.915282291 + 4.4 v = 4.915282291 + 4.4 Combine like terms: 4.915282291 + 4.4 = 9.315282291 v = 9.315282291 Simplifying v = 9.315282291Subproblem 2
v + -4.4 = -4.915282291 Simplifying v + -4.4 = -4.915282291 Reorder the terms: -4.4 + v = -4.915282291 Solving -4.4 + v = -4.915282291 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '4.4' to each side of the equation. -4.4 + 4.4 + v = -4.915282291 + 4.4 Combine like terms: -4.4 + 4.4 = 0.0 0.0 + v = -4.915282291 + 4.4 v = -4.915282291 + 4.4 Combine like terms: -4.915282291 + 4.4 = -0.515282291 v = -0.515282291 Simplifying v = -0.515282291Solution
The solution to the problem is based on the solutions from the subproblems. v = {9.315282291, -0.515282291}
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