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Simplifying (0.6) * x2 + (0.875) * x + (-0.225) = 0 0.6x2 + 0.875x + -0.225 = 0 Reorder the terms: -0.225 + 0.875x + 0.6x2 = 0 Solving -0.225 + 0.875x + 0.6x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.6 the coefficient of the squared term: Divide each side by '0.6'. -0.375 + 1.458333333x + x2 = 0 Move the constant term to the right: Add '0.375' to each side of the equation. -0.375 + 1.458333333x + 0.375 + x2 = 0 + 0.375 Reorder the terms: -0.375 + 0.375 + 1.458333333x + x2 = 0 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + 1.458333333x + x2 = 0 + 0.375 1.458333333x + x2 = 0 + 0.375 Combine like terms: 0 + 0.375 = 0.375 1.458333333x + x2 = 0.375 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 = 0.375 + 0.5316840275 Reorder the terms: 0.5316840275 + 1.458333333x + x2 = 0.375 + 0.5316840275 Combine like terms: 0.375 + 0.5316840275 = 0.9066840275 0.5316840275 + 1.458333333x + x2 = 0.9066840275 Factor a perfect square on the left side: (x + 0.7291666665)(x + 0.7291666665) = 0.9066840275 Calculate the square root of the right side: 0.952199573 Break this problem into two subproblems by setting (x + 0.7291666665) equal to 0.952199573 and -0.952199573.Subproblem 1
x + 0.7291666665 = 0.952199573 Simplifying x + 0.7291666665 = 0.952199573 Reorder the terms: 0.7291666665 + x = 0.952199573 Solving 0.7291666665 + x = 0.952199573 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 = 0.952199573 + -0.7291666665 Combine like terms: 0.7291666665 + -0.7291666665 = 0.0000000000 0.0000000000 + x = 0.952199573 + -0.7291666665 x = 0.952199573 + -0.7291666665 Combine like terms: 0.952199573 + -0.7291666665 = 0.2230329065 x = 0.2230329065 Simplifying x = 0.2230329065Subproblem 2
x + 0.7291666665 = -0.952199573 Simplifying x + 0.7291666665 = -0.952199573 Reorder the terms: 0.7291666665 + x = -0.952199573 Solving 0.7291666665 + x = -0.952199573 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 = -0.952199573 + -0.7291666665 Combine like terms: 0.7291666665 + -0.7291666665 = 0.0000000000 0.0000000000 + x = -0.952199573 + -0.7291666665 x = -0.952199573 + -0.7291666665 Combine like terms: -0.952199573 + -0.7291666665 = -1.6813662395 x = -1.6813662395 Simplifying x = -1.6813662395Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.2230329065, -1.6813662395}
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