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Simplifying (v + 7)(v + -8) = 2 Reorder the terms: (7 + v)(v + -8) = 2 Reorder the terms: (7 + v)(-8 + v) = 2 Multiply (7 + v) * (-8 + v) (7(-8 + v) + v(-8 + v)) = 2 ((-8 * 7 + v * 7) + v(-8 + v)) = 2 ((-56 + 7v) + v(-8 + v)) = 2 (-56 + 7v + (-8 * v + v * v)) = 2 (-56 + 7v + (-8v + v2)) = 2 Combine like terms: 7v + -8v = -1v (-56 + -1v + v2) = 2 Solving -56 + -1v + v2 = 2 Solving for variable 'v'. Reorder the terms: -56 + -2 + -1v + v2 = 2 + -2 Combine like terms: -56 + -2 = -58 -58 + -1v + v2 = 2 + -2 Combine like terms: 2 + -2 = 0 -58 + -1v + v2 = 0 Begin completing the square. Move the constant term to the right: Add '58' to each side of the equation. -58 + -1v + 58 + v2 = 0 + 58 Reorder the terms: -58 + 58 + -1v + v2 = 0 + 58 Combine like terms: -58 + 58 = 0 0 + -1v + v2 = 0 + 58 -1v + v2 = 0 + 58 Combine like terms: 0 + 58 = 58 -1v + v2 = 58 The v term is -1v. 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. -1v + 0.25 + v2 = 58 + 0.25 Reorder the terms: 0.25 + -1v + v2 = 58 + 0.25 Combine like terms: 58 + 0.25 = 58.25 0.25 + -1v + v2 = 58.25 Factor a perfect square on the left side: (v + -0.5)(v + -0.5) = 58.25 Calculate the square root of the right side: 7.632168761 Break this problem into two subproblems by setting (v + -0.5) equal to 7.632168761 and -7.632168761.Subproblem 1
v + -0.5 = 7.632168761 Simplifying v + -0.5 = 7.632168761 Reorder the terms: -0.5 + v = 7.632168761 Solving -0.5 + v = 7.632168761 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 = 7.632168761 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + v = 7.632168761 + 0.5 v = 7.632168761 + 0.5 Combine like terms: 7.632168761 + 0.5 = 8.132168761 v = 8.132168761 Simplifying v = 8.132168761Subproblem 2
v + -0.5 = -7.632168761 Simplifying v + -0.5 = -7.632168761 Reorder the terms: -0.5 + v = -7.632168761 Solving -0.5 + v = -7.632168761 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 = -7.632168761 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + v = -7.632168761 + 0.5 v = -7.632168761 + 0.5 Combine like terms: -7.632168761 + 0.5 = -7.132168761 v = -7.132168761 Simplifying v = -7.132168761Solution
The solution to the problem is based on the solutions from the subproblems. v = {8.132168761, -7.132168761}
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