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Simplifying v(v + -30.5) + (v + -26.8) = 201.8 Reorder the terms: v(-30.5 + v) + (v + -26.8) = 201.8 (-30.5 * v + v * v) + (v + -26.8) = 201.8 (-30.5v + v2) + (v + -26.8) = 201.8 Reorder the terms: -30.5v + v2 + (-26.8 + v) = 201.8 Remove parenthesis around (-26.8 + v) -30.5v + v2 + -26.8 + v = 201.8 Reorder the terms: -26.8 + -30.5v + v + v2 = 201.8 Combine like terms: -30.5v + v = -29.5v -26.8 + -29.5v + v2 = 201.8 Solving -26.8 + -29.5v + v2 = 201.8 Solving for variable 'v'. Reorder the terms: -26.8 + -201.8 + -29.5v + v2 = 201.8 + -201.8 Combine like terms: -26.8 + -201.8 = -228.6 -228.6 + -29.5v + v2 = 201.8 + -201.8 Combine like terms: 201.8 + -201.8 = 0.0 -228.6 + -29.5v + v2 = 0.0 Begin completing the square. Move the constant term to the right: Add '228.6' to each side of the equation. -228.6 + -29.5v + 228.6 + v2 = 0.0 + 228.6 Reorder the terms: -228.6 + 228.6 + -29.5v + v2 = 0.0 + 228.6 Combine like terms: -228.6 + 228.6 = 0.0 0.0 + -29.5v + v2 = 0.0 + 228.6 -29.5v + v2 = 0.0 + 228.6 Combine like terms: 0.0 + 228.6 = 228.6 -29.5v + v2 = 228.6 The v term is -29.5v. Take half its coefficient (-14.75). Square it (217.5625) and add it to both sides. Add '217.5625' to each side of the equation. -29.5v + 217.5625 + v2 = 228.6 + 217.5625 Reorder the terms: 217.5625 + -29.5v + v2 = 228.6 + 217.5625 Combine like terms: 228.6 + 217.5625 = 446.1625 217.5625 + -29.5v + v2 = 446.1625 Factor a perfect square on the left side: (v + -14.75)(v + -14.75) = 446.1625 Calculate the square root of the right side: 21.122559031 Break this problem into two subproblems by setting (v + -14.75) equal to 21.122559031 and -21.122559031.Subproblem 1
v + -14.75 = 21.122559031 Simplifying v + -14.75 = 21.122559031 Reorder the terms: -14.75 + v = 21.122559031 Solving -14.75 + v = 21.122559031 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '14.75' to each side of the equation. -14.75 + 14.75 + v = 21.122559031 + 14.75 Combine like terms: -14.75 + 14.75 = 0.00 0.00 + v = 21.122559031 + 14.75 v = 21.122559031 + 14.75 Combine like terms: 21.122559031 + 14.75 = 35.872559031 v = 35.872559031 Simplifying v = 35.872559031Subproblem 2
v + -14.75 = -21.122559031 Simplifying v + -14.75 = -21.122559031 Reorder the terms: -14.75 + v = -21.122559031 Solving -14.75 + v = -21.122559031 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '14.75' to each side of the equation. -14.75 + 14.75 + v = -21.122559031 + 14.75 Combine like terms: -14.75 + 14.75 = 0.00 0.00 + v = -21.122559031 + 14.75 v = -21.122559031 + 14.75 Combine like terms: -21.122559031 + 14.75 = -6.372559031 v = -6.372559031 Simplifying v = -6.372559031Solution
The solution to the problem is based on the solutions from the subproblems. v = {35.872559031, -6.372559031}
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