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Simplifying 24x2 + -35x + -11 = -3 Reorder the terms: -11 + -35x + 24x2 = -3 Solving -11 + -35x + 24x2 = -3 Solving for variable 'x'. Reorder the terms: -11 + 3 + -35x + 24x2 = -3 + 3 Combine like terms: -11 + 3 = -8 -8 + -35x + 24x2 = -3 + 3 Combine like terms: -3 + 3 = 0 -8 + -35x + 24x2 = 0 Begin completing the square. Divide all terms by 24 the coefficient of the squared term: Divide each side by '24'. -0.3333333333 + -1.458333333x + x2 = 0 Move the constant term to the right: Add '0.3333333333' to each side of the equation. -0.3333333333 + -1.458333333x + 0.3333333333 + x2 = 0 + 0.3333333333 Reorder the terms: -0.3333333333 + 0.3333333333 + -1.458333333x + x2 = 0 + 0.3333333333 Combine like terms: -0.3333333333 + 0.3333333333 = 0.0000000000 0.0000000000 + -1.458333333x + x2 = 0 + 0.3333333333 -1.458333333x + x2 = 0 + 0.3333333333 Combine like terms: 0 + 0.3333333333 = 0.3333333333 -1.458333333x + x2 = 0.3333333333 The x term is -1.458333333x. Take half its coefficient (-0.7291666665). Square it (0.5316840275) and add it to both sides. Add '0.5316840275' to each side of the equation. -1.458333333x + 0.5316840275 + x2 = 0.3333333333 + 0.5316840275 Reorder the terms: 0.5316840275 + -1.458333333x + x2 = 0.3333333333 + 0.5316840275 Combine like terms: 0.3333333333 + 0.5316840275 = 0.8650173608 0.5316840275 + -1.458333333x + x2 = 0.8650173608 Factor a perfect square on the left side: (x + -0.7291666665)(x + -0.7291666665) = 0.8650173608 Calculate the square root of the right side: 0.930063095 Break this problem into two subproblems by setting (x + -0.7291666665) equal to 0.930063095 and -0.930063095.Subproblem 1
x + -0.7291666665 = 0.930063095 Simplifying x + -0.7291666665 = 0.930063095 Reorder the terms: -0.7291666665 + x = 0.930063095 Solving -0.7291666665 + x = 0.930063095 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.7291666665' to each side of the equation. -0.7291666665 + 0.7291666665 + x = 0.930063095 + 0.7291666665 Combine like terms: -0.7291666665 + 0.7291666665 = 0.0000000000 0.0000000000 + x = 0.930063095 + 0.7291666665 x = 0.930063095 + 0.7291666665 Combine like terms: 0.930063095 + 0.7291666665 = 1.6592297615 x = 1.6592297615 Simplifying x = 1.6592297615Subproblem 2
x + -0.7291666665 = -0.930063095 Simplifying x + -0.7291666665 = -0.930063095 Reorder the terms: -0.7291666665 + x = -0.930063095 Solving -0.7291666665 + x = -0.930063095 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.7291666665' to each side of the equation. -0.7291666665 + 0.7291666665 + x = -0.930063095 + 0.7291666665 Combine like terms: -0.7291666665 + 0.7291666665 = 0.0000000000 0.0000000000 + x = -0.930063095 + 0.7291666665 x = -0.930063095 + 0.7291666665 Combine like terms: -0.930063095 + 0.7291666665 = -0.2008964285 x = -0.2008964285 Simplifying x = -0.2008964285Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.6592297615, -0.2008964285}
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