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Simplifying 900x2 + -54x + -900 = 0 Reorder the terms: -900 + -54x + 900x2 = 0 Solving -900 + -54x + 900x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '18'. 18(-50 + -3x + 50x2) = 0 Ignore the factor 18.Subproblem 1
Set the factor '(-50 + -3x + 50x2)' equal to zero and attempt to solve: Simplifying -50 + -3x + 50x2 = 0 Solving -50 + -3x + 50x2 = 0 Begin completing the square. Divide all terms by 50 the coefficient of the squared term: Divide each side by '50'. -1 + -0.06x + x2 = 0.0 Move the constant term to the right: Add '1' to each side of the equation. -1 + -0.06x + 1 + x2 = 0.0 + 1 Reorder the terms: -1 + 1 + -0.06x + x2 = 0.0 + 1 Combine like terms: -1 + 1 = 0 0 + -0.06x + x2 = 0.0 + 1 -0.06x + x2 = 0.0 + 1 Combine like terms: 0.0 + 1 = 1 -0.06x + x2 = 1 The x term is -0.06x. Take half its coefficient (-0.03). Square it (0.0009) and add it to both sides. Add '0.0009' to each side of the equation. -0.06x + 0.0009 + x2 = 1 + 0.0009 Reorder the terms: 0.0009 + -0.06x + x2 = 1 + 0.0009 Combine like terms: 1 + 0.0009 = 1.0009 0.0009 + -0.06x + x2 = 1.0009 Factor a perfect square on the left side: (x + -0.03)(x + -0.03) = 1.0009 Calculate the square root of the right side: 1.000449899 Break this problem into two subproblems by setting (x + -0.03) equal to 1.000449899 and -1.000449899.Subproblem 1
x + -0.03 = 1.000449899 Simplifying x + -0.03 = 1.000449899 Reorder the terms: -0.03 + x = 1.000449899 Solving -0.03 + x = 1.000449899 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.03' to each side of the equation. -0.03 + 0.03 + x = 1.000449899 + 0.03 Combine like terms: -0.03 + 0.03 = 0.00 0.00 + x = 1.000449899 + 0.03 x = 1.000449899 + 0.03 Combine like terms: 1.000449899 + 0.03 = 1.030449899 x = 1.030449899 Simplifying x = 1.030449899Subproblem 2
x + -0.03 = -1.000449899 Simplifying x + -0.03 = -1.000449899 Reorder the terms: -0.03 + x = -1.000449899 Solving -0.03 + x = -1.000449899 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.03' to each side of the equation. -0.03 + 0.03 + x = -1.000449899 + 0.03 Combine like terms: -0.03 + 0.03 = 0.00 0.00 + x = -1.000449899 + 0.03 x = -1.000449899 + 0.03 Combine like terms: -1.000449899 + 0.03 = -0.970449899 x = -0.970449899 Simplifying x = -0.970449899Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.030449899, -0.970449899}Solution
x = {1.030449899, -0.970449899}
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