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Simplifying -40000x2 + 8820x + 190000 = 0 Reorder the terms: 190000 + 8820x + -40000x2 = 0 Solving 190000 + 8820x + -40000x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '20'. 20(9500 + 441x + -2000x2) = 0 Ignore the factor 20.Subproblem 1
Set the factor '(9500 + 441x + -2000x2)' equal to zero and attempt to solve: Simplifying 9500 + 441x + -2000x2 = 0 Solving 9500 + 441x + -2000x2 = 0 Begin completing the square. Divide all terms by -2000 the coefficient of the squared term: Divide each side by '-2000'. -4.75 + -0.2205x + x2 = 0.000 Move the constant term to the right: Add '4.75' to each side of the equation. -4.75 + -0.2205x + 4.75 + x2 = 0.000 + 4.75 Reorder the terms: -4.75 + 4.75 + -0.2205x + x2 = 0.000 + 4.75 Combine like terms: -4.75 + 4.75 = 0.00 0.00 + -0.2205x + x2 = 0.000 + 4.75 -0.2205x + x2 = 0.000 + 4.75 Combine like terms: 0.000 + 4.75 = 4.75 -0.2205x + x2 = 4.75 The x term is -0.2205x. Take half its coefficient (-0.11025). Square it (0.0121550625) and add it to both sides. Add '0.0121550625' to each side of the equation. -0.2205x + 0.0121550625 + x2 = 4.75 + 0.0121550625 Reorder the terms: 0.0121550625 + -0.2205x + x2 = 4.75 + 0.0121550625 Combine like terms: 4.75 + 0.0121550625 = 4.7621550625 0.0121550625 + -0.2205x + x2 = 4.7621550625 Factor a perfect square on the left side: (x + -0.11025)(x + -0.11025) = 4.7621550625 Calculate the square root of the right side: 2.182236253 Break this problem into two subproblems by setting (x + -0.11025) equal to 2.182236253 and -2.182236253.Subproblem 1
x + -0.11025 = 2.182236253 Simplifying x + -0.11025 = 2.182236253 Reorder the terms: -0.11025 + x = 2.182236253 Solving -0.11025 + x = 2.182236253 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.11025' to each side of the equation. -0.11025 + 0.11025 + x = 2.182236253 + 0.11025 Combine like terms: -0.11025 + 0.11025 = 0.00000 0.00000 + x = 2.182236253 + 0.11025 x = 2.182236253 + 0.11025 Combine like terms: 2.182236253 + 0.11025 = 2.292486253 x = 2.292486253 Simplifying x = 2.292486253Subproblem 2
x + -0.11025 = -2.182236253 Simplifying x + -0.11025 = -2.182236253 Reorder the terms: -0.11025 + x = -2.182236253 Solving -0.11025 + x = -2.182236253 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.11025' to each side of the equation. -0.11025 + 0.11025 + x = -2.182236253 + 0.11025 Combine like terms: -0.11025 + 0.11025 = 0.00000 0.00000 + x = -2.182236253 + 0.11025 x = -2.182236253 + 0.11025 Combine like terms: -2.182236253 + 0.11025 = -2.071986253 x = -2.071986253 Simplifying x = -2.071986253Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.292486253, -2.071986253}Solution
x = {2.292486253, -2.071986253}
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