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Simplifying 2x2 + -23x = 20 Reorder the terms: -23x + 2x2 = 20 Solving -23x + 2x2 = 20 Solving for variable 'x'. Reorder the terms: -20 + -23x + 2x2 = 20 + -20 Combine like terms: 20 + -20 = 0 -20 + -23x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -10 + -11.5x + x2 = 0 Move the constant term to the right: Add '10' to each side of the equation. -10 + -11.5x + 10 + x2 = 0 + 10 Reorder the terms: -10 + 10 + -11.5x + x2 = 0 + 10 Combine like terms: -10 + 10 = 0 0 + -11.5x + x2 = 0 + 10 -11.5x + x2 = 0 + 10 Combine like terms: 0 + 10 = 10 -11.5x + x2 = 10 The x term is -11.5x. Take half its coefficient (-5.75). Square it (33.0625) and add it to both sides. Add '33.0625' to each side of the equation. -11.5x + 33.0625 + x2 = 10 + 33.0625 Reorder the terms: 33.0625 + -11.5x + x2 = 10 + 33.0625 Combine like terms: 10 + 33.0625 = 43.0625 33.0625 + -11.5x + x2 = 43.0625 Factor a perfect square on the left side: (x + -5.75)(x + -5.75) = 43.0625 Calculate the square root of the right side: 6.562202374 Break this problem into two subproblems by setting (x + -5.75) equal to 6.562202374 and -6.562202374.Subproblem 1
x + -5.75 = 6.562202374 Simplifying x + -5.75 = 6.562202374 Reorder the terms: -5.75 + x = 6.562202374 Solving -5.75 + x = 6.562202374 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.75' to each side of the equation. -5.75 + 5.75 + x = 6.562202374 + 5.75 Combine like terms: -5.75 + 5.75 = 0.00 0.00 + x = 6.562202374 + 5.75 x = 6.562202374 + 5.75 Combine like terms: 6.562202374 + 5.75 = 12.312202374 x = 12.312202374 Simplifying x = 12.312202374Subproblem 2
x + -5.75 = -6.562202374 Simplifying x + -5.75 = -6.562202374 Reorder the terms: -5.75 + x = -6.562202374 Solving -5.75 + x = -6.562202374 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.75' to each side of the equation. -5.75 + 5.75 + x = -6.562202374 + 5.75 Combine like terms: -5.75 + 5.75 = 0.00 0.00 + x = -6.562202374 + 5.75 x = -6.562202374 + 5.75 Combine like terms: -6.562202374 + 5.75 = -0.812202374 x = -0.812202374 Simplifying x = -0.812202374Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.312202374, -0.812202374}
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