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Simplifying 2x2 = 777x + 4 Reorder the terms: 2x2 = 4 + 777x Solving 2x2 = 4 + 777x Solving for variable 'x'. Reorder the terms: -4 + -777x + 2x2 = 4 + 777x + -4 + -777x Reorder the terms: -4 + -777x + 2x2 = 4 + -4 + 777x + -777x Combine like terms: 4 + -4 = 0 -4 + -777x + 2x2 = 0 + 777x + -777x -4 + -777x + 2x2 = 777x + -777x Combine like terms: 777x + -777x = 0 -4 + -777x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -2 + -388.5x + x2 = 0 Move the constant term to the right: Add '2' to each side of the equation. -2 + -388.5x + 2 + x2 = 0 + 2 Reorder the terms: -2 + 2 + -388.5x + x2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -388.5x + x2 = 0 + 2 -388.5x + x2 = 0 + 2 Combine like terms: 0 + 2 = 2 -388.5x + x2 = 2 The x term is -388.5x. Take half its coefficient (-194.25). Square it (37733.0625) and add it to both sides. Add '37733.0625' to each side of the equation. -388.5x + 37733.0625 + x2 = 2 + 37733.0625 Reorder the terms: 37733.0625 + -388.5x + x2 = 2 + 37733.0625 Combine like terms: 2 + 37733.0625 = 37735.0625 37733.0625 + -388.5x + x2 = 37735.0625 Factor a perfect square on the left side: (x + -194.25)(x + -194.25) = 37735.0625 Calculate the square root of the right side: 194.255147937 Break this problem into two subproblems by setting (x + -194.25) equal to 194.255147937 and -194.255147937.Subproblem 1
x + -194.25 = 194.255147937 Simplifying x + -194.25 = 194.255147937 Reorder the terms: -194.25 + x = 194.255147937 Solving -194.25 + x = 194.255147937 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '194.25' to each side of the equation. -194.25 + 194.25 + x = 194.255147937 + 194.25 Combine like terms: -194.25 + 194.25 = 0.00 0.00 + x = 194.255147937 + 194.25 x = 194.255147937 + 194.25 Combine like terms: 194.255147937 + 194.25 = 388.505147937 x = 388.505147937 Simplifying x = 388.505147937Subproblem 2
x + -194.25 = -194.255147937 Simplifying x + -194.25 = -194.255147937 Reorder the terms: -194.25 + x = -194.255147937 Solving -194.25 + x = -194.255147937 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '194.25' to each side of the equation. -194.25 + 194.25 + x = -194.255147937 + 194.25 Combine like terms: -194.25 + 194.25 = 0.00 0.00 + x = -194.255147937 + 194.25 x = -194.255147937 + 194.25 Combine like terms: -194.255147937 + 194.25 = -0.005147937 x = -0.005147937 Simplifying x = -0.005147937Solution
The solution to the problem is based on the solutions from the subproblems. x = {388.505147937, -0.005147937}
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