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Simplifying 0.52x2 + -0.282x + 0.0116 = x2 + -0.545x + 0.0225 Reorder the terms: 0.0116 + -0.282x + 0.52x2 = x2 + -0.545x + 0.0225 Reorder the terms: 0.0116 + -0.282x + 0.52x2 = 0.0225 + -0.545x + x2 Solving 0.0116 + -0.282x + 0.52x2 = 0.0225 + -0.545x + x2 Solving for variable 'x'. Reorder the terms: 0.0116 + -0.0225 + -0.282x + 0.545x + 0.52x2 + -1x2 = 0.0225 + -0.545x + x2 + -0.0225 + 0.545x + -1x2 Combine like terms: 0.0116 + -0.0225 = -0.0109 -0.0109 + -0.282x + 0.545x + 0.52x2 + -1x2 = 0.0225 + -0.545x + x2 + -0.0225 + 0.545x + -1x2 Combine like terms: -0.282x + 0.545x = 0.263x -0.0109 + 0.263x + 0.52x2 + -1x2 = 0.0225 + -0.545x + x2 + -0.0225 + 0.545x + -1x2 Combine like terms: 0.52x2 + -1x2 = -0.48x2 -0.0109 + 0.263x + -0.48x2 = 0.0225 + -0.545x + x2 + -0.0225 + 0.545x + -1x2 Reorder the terms: -0.0109 + 0.263x + -0.48x2 = 0.0225 + -0.0225 + -0.545x + 0.545x + x2 + -1x2 Combine like terms: 0.0225 + -0.0225 = 0.0000 -0.0109 + 0.263x + -0.48x2 = 0.0000 + -0.545x + 0.545x + x2 + -1x2 -0.0109 + 0.263x + -0.48x2 = -0.545x + 0.545x + x2 + -1x2 Combine like terms: -0.545x + 0.545x = 0.000 -0.0109 + 0.263x + -0.48x2 = 0.000 + x2 + -1x2 -0.0109 + 0.263x + -0.48x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -0.0109 + 0.263x + -0.48x2 = 0 Begin completing the square. Divide all terms by -0.48 the coefficient of the squared term: Divide each side by '-0.48'. 0.02270833333 + -0.5479166667x + x2 = 0 Move the constant term to the right: Add '-0.02270833333' to each side of the equation. 0.02270833333 + -0.5479166667x + -0.02270833333 + x2 = 0 + -0.02270833333 Reorder the terms: 0.02270833333 + -0.02270833333 + -0.5479166667x + x2 = 0 + -0.02270833333 Combine like terms: 0.02270833333 + -0.02270833333 = 0.00000000000 0.00000000000 + -0.5479166667x + x2 = 0 + -0.02270833333 -0.5479166667x + x2 = 0 + -0.02270833333 Combine like terms: 0 + -0.02270833333 = -0.02270833333 -0.5479166667x + x2 = -0.02270833333 The x term is -0.5479166667x. Take half its coefficient (-0.2739583334). Square it (0.07505316844) and add it to both sides. Add '0.07505316844' to each side of the equation. -0.5479166667x + 0.07505316844 + x2 = -0.02270833333 + 0.07505316844 Reorder the terms: 0.07505316844 + -0.5479166667x + x2 = -0.02270833333 + 0.07505316844 Combine like terms: -0.02270833333 + 0.07505316844 = 0.05234483511 0.07505316844 + -0.5479166667x + x2 = 0.05234483511 Factor a perfect square on the left side: (x + -0.2739583334)(x + -0.2739583334) = 0.05234483511 Calculate the square root of the right side: 0.228789937 Break this problem into two subproblems by setting (x + -0.2739583334) equal to 0.228789937 and -0.228789937.Subproblem 1
x + -0.2739583334 = 0.228789937 Simplifying x + -0.2739583334 = 0.228789937 Reorder the terms: -0.2739583334 + x = 0.228789937 Solving -0.2739583334 + x = 0.228789937 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2739583334' to each side of the equation. -0.2739583334 + 0.2739583334 + x = 0.228789937 + 0.2739583334 Combine like terms: -0.2739583334 + 0.2739583334 = 0.0000000000 0.0000000000 + x = 0.228789937 + 0.2739583334 x = 0.228789937 + 0.2739583334 Combine like terms: 0.228789937 + 0.2739583334 = 0.5027482704 x = 0.5027482704 Simplifying x = 0.5027482704Subproblem 2
x + -0.2739583334 = -0.228789937 Simplifying x + -0.2739583334 = -0.228789937 Reorder the terms: -0.2739583334 + x = -0.228789937 Solving -0.2739583334 + x = -0.228789937 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2739583334' to each side of the equation. -0.2739583334 + 0.2739583334 + x = -0.228789937 + 0.2739583334 Combine like terms: -0.2739583334 + 0.2739583334 = 0.0000000000 0.0000000000 + x = -0.228789937 + 0.2739583334 x = -0.228789937 + 0.2739583334 Combine like terms: -0.228789937 + 0.2739583334 = 0.0451683964 x = 0.0451683964 Simplifying x = 0.0451683964Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.5027482704, 0.0451683964}
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