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Simplifying 35x + -24x2 + 3 = 0 Reorder the terms: 3 + 35x + -24x2 = 0 Solving 3 + 35x + -24x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -24 the coefficient of the squared term: Divide each side by '-24'. -0.125 + -1.458333333x + x2 = 0 Move the constant term to the right: Add '0.125' to each side of the equation. -0.125 + -1.458333333x + 0.125 + x2 = 0 + 0.125 Reorder the terms: -0.125 + 0.125 + -1.458333333x + x2 = 0 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + -1.458333333x + x2 = 0 + 0.125 -1.458333333x + x2 = 0 + 0.125 Combine like terms: 0 + 0.125 = 0.125 -1.458333333x + x2 = 0.125 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 = 0.125 + 0.5316840275 Reorder the terms: 0.5316840275 + -1.458333333x + x2 = 0.125 + 0.5316840275 Combine like terms: 0.125 + 0.5316840275 = 0.6566840275 0.5316840275 + -1.458333333x + x2 = 0.6566840275 Factor a perfect square on the left side: (x + -0.7291666665)(x + -0.7291666665) = 0.6566840275 Calculate the square root of the right side: 0.810360431 Break this problem into two subproblems by setting (x + -0.7291666665) equal to 0.810360431 and -0.810360431.Subproblem 1
x + -0.7291666665 = 0.810360431 Simplifying x + -0.7291666665 = 0.810360431 Reorder the terms: -0.7291666665 + x = 0.810360431 Solving -0.7291666665 + x = 0.810360431 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 = 0.810360431 + 0.7291666665 Combine like terms: -0.7291666665 + 0.7291666665 = 0.0000000000 0.0000000000 + x = 0.810360431 + 0.7291666665 x = 0.810360431 + 0.7291666665 Combine like terms: 0.810360431 + 0.7291666665 = 1.5395270975 x = 1.5395270975 Simplifying x = 1.5395270975Subproblem 2
x + -0.7291666665 = -0.810360431 Simplifying x + -0.7291666665 = -0.810360431 Reorder the terms: -0.7291666665 + x = -0.810360431 Solving -0.7291666665 + x = -0.810360431 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 = -0.810360431 + 0.7291666665 Combine like terms: -0.7291666665 + 0.7291666665 = 0.0000000000 0.0000000000 + x = -0.810360431 + 0.7291666665 x = -0.810360431 + 0.7291666665 Combine like terms: -0.810360431 + 0.7291666665 = -0.0811937645 x = -0.0811937645 Simplifying x = -0.0811937645Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.5395270975, -0.0811937645}
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