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Simplifying 12v2 + -15v + -7 = 0 Reorder the terms: -7 + -15v + 12v2 = 0 Solving -7 + -15v + 12v2 = 0 Solving for variable 'v'. Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. -0.5833333333 + -1.25v + v2 = 0 Move the constant term to the right: Add '0.5833333333' to each side of the equation. -0.5833333333 + -1.25v + 0.5833333333 + v2 = 0 + 0.5833333333 Reorder the terms: -0.5833333333 + 0.5833333333 + -1.25v + v2 = 0 + 0.5833333333 Combine like terms: -0.5833333333 + 0.5833333333 = 0.0000000000 0.0000000000 + -1.25v + v2 = 0 + 0.5833333333 -1.25v + v2 = 0 + 0.5833333333 Combine like terms: 0 + 0.5833333333 = 0.5833333333 -1.25v + v2 = 0.5833333333 The v term is -1.25v. Take half its coefficient (-0.625). Square it (0.390625) and add it to both sides. Add '0.390625' to each side of the equation. -1.25v + 0.390625 + v2 = 0.5833333333 + 0.390625 Reorder the terms: 0.390625 + -1.25v + v2 = 0.5833333333 + 0.390625 Combine like terms: 0.5833333333 + 0.390625 = 0.9739583333 0.390625 + -1.25v + v2 = 0.9739583333 Factor a perfect square on the left side: (v + -0.625)(v + -0.625) = 0.9739583333 Calculate the square root of the right side: 0.986893274 Break this problem into two subproblems by setting (v + -0.625) equal to 0.986893274 and -0.986893274.Subproblem 1
v + -0.625 = 0.986893274 Simplifying v + -0.625 = 0.986893274 Reorder the terms: -0.625 + v = 0.986893274 Solving -0.625 + v = 0.986893274 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '0.625' to each side of the equation. -0.625 + 0.625 + v = 0.986893274 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + v = 0.986893274 + 0.625 v = 0.986893274 + 0.625 Combine like terms: 0.986893274 + 0.625 = 1.611893274 v = 1.611893274 Simplifying v = 1.611893274Subproblem 2
v + -0.625 = -0.986893274 Simplifying v + -0.625 = -0.986893274 Reorder the terms: -0.625 + v = -0.986893274 Solving -0.625 + v = -0.986893274 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '0.625' to each side of the equation. -0.625 + 0.625 + v = -0.986893274 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + v = -0.986893274 + 0.625 v = -0.986893274 + 0.625 Combine like terms: -0.986893274 + 0.625 = -0.361893274 v = -0.361893274 Simplifying v = -0.361893274Solution
The solution to the problem is based on the solutions from the subproblems. v = {1.611893274, -0.361893274}
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