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Simplifying 2x2 + 102x + 210 = 0 Reorder the terms: 210 + 102x + 2x2 = 0 Solving 210 + 102x + 2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(105 + 51x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(105 + 51x + x2)' equal to zero and attempt to solve: Simplifying 105 + 51x + x2 = 0 Solving 105 + 51x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-105' to each side of the equation. 105 + 51x + -105 + x2 = 0 + -105 Reorder the terms: 105 + -105 + 51x + x2 = 0 + -105 Combine like terms: 105 + -105 = 0 0 + 51x + x2 = 0 + -105 51x + x2 = 0 + -105 Combine like terms: 0 + -105 = -105 51x + x2 = -105 The x term is 51x. Take half its coefficient (25.5). Square it (650.25) and add it to both sides. Add '650.25' to each side of the equation. 51x + 650.25 + x2 = -105 + 650.25 Reorder the terms: 650.25 + 51x + x2 = -105 + 650.25 Combine like terms: -105 + 650.25 = 545.25 650.25 + 51x + x2 = 545.25 Factor a perfect square on the left side: (x + 25.5)(x + 25.5) = 545.25 Calculate the square root of the right side: 23.350588858 Break this problem into two subproblems by setting (x + 25.5) equal to 23.350588858 and -23.350588858.Subproblem 1
x + 25.5 = 23.350588858 Simplifying x + 25.5 = 23.350588858 Reorder the terms: 25.5 + x = 23.350588858 Solving 25.5 + x = 23.350588858 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-25.5' to each side of the equation. 25.5 + -25.5 + x = 23.350588858 + -25.5 Combine like terms: 25.5 + -25.5 = 0.0 0.0 + x = 23.350588858 + -25.5 x = 23.350588858 + -25.5 Combine like terms: 23.350588858 + -25.5 = -2.149411142 x = -2.149411142 Simplifying x = -2.149411142Subproblem 2
x + 25.5 = -23.350588858 Simplifying x + 25.5 = -23.350588858 Reorder the terms: 25.5 + x = -23.350588858 Solving 25.5 + x = -23.350588858 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-25.5' to each side of the equation. 25.5 + -25.5 + x = -23.350588858 + -25.5 Combine like terms: 25.5 + -25.5 = 0.0 0.0 + x = -23.350588858 + -25.5 x = -23.350588858 + -25.5 Combine like terms: -23.350588858 + -25.5 = -48.850588858 x = -48.850588858 Simplifying x = -48.850588858Solution
The solution to the problem is based on the solutions from the subproblems. x = {-2.149411142, -48.850588858}Solution
x = {-2.149411142, -48.850588858}
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