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Simplifying 6.240567922x2 + -6.582717787x + 0.096149865 = 0 Reorder the terms: 0.096149865 + -6.582717787x + 6.240567922x2 = 0 Solving 0.096149865 + -6.582717787x + 6.240567922x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 6.240567922 the coefficient of the squared term: Divide each side by '6.240567922'. 0.01540722995 + -1.054826719x + x2 = 0 Move the constant term to the right: Add '-0.01540722995' to each side of the equation. 0.01540722995 + -1.054826719x + -0.01540722995 + x2 = 0 + -0.01540722995 Reorder the terms: 0.01540722995 + -0.01540722995 + -1.054826719x + x2 = 0 + -0.01540722995 Combine like terms: 0.01540722995 + -0.01540722995 = 0.00000000000 0.00000000000 + -1.054826719x + x2 = 0 + -0.01540722995 -1.054826719x + x2 = 0 + -0.01540722995 Combine like terms: 0 + -0.01540722995 = -0.01540722995 -1.054826719x + x2 = -0.01540722995 The x term is -1.054826719x. Take half its coefficient (-0.5274133595). Square it (0.2781648518) and add it to both sides. Add '0.2781648518' to each side of the equation. -1.054826719x + 0.2781648518 + x2 = -0.01540722995 + 0.2781648518 Reorder the terms: 0.2781648518 + -1.054826719x + x2 = -0.01540722995 + 0.2781648518 Combine like terms: -0.01540722995 + 0.2781648518 = 0.26275762185 0.2781648518 + -1.054826719x + x2 = 0.26275762185 Factor a perfect square on the left side: (x + -0.5274133595)(x + -0.5274133595) = 0.26275762185 Calculate the square root of the right side: 0.51259889 Break this problem into two subproblems by setting (x + -0.5274133595) equal to 0.51259889 and -0.51259889.Subproblem 1
x + -0.5274133595 = 0.51259889 Simplifying x + -0.5274133595 = 0.51259889 Reorder the terms: -0.5274133595 + x = 0.51259889 Solving -0.5274133595 + x = 0.51259889 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5274133595' to each side of the equation. -0.5274133595 + 0.5274133595 + x = 0.51259889 + 0.5274133595 Combine like terms: -0.5274133595 + 0.5274133595 = 0.0000000000 0.0000000000 + x = 0.51259889 + 0.5274133595 x = 0.51259889 + 0.5274133595 Combine like terms: 0.51259889 + 0.5274133595 = 1.0400122495 x = 1.0400122495 Simplifying x = 1.0400122495Subproblem 2
x + -0.5274133595 = -0.51259889 Simplifying x + -0.5274133595 = -0.51259889 Reorder the terms: -0.5274133595 + x = -0.51259889 Solving -0.5274133595 + x = -0.51259889 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5274133595' to each side of the equation. -0.5274133595 + 0.5274133595 + x = -0.51259889 + 0.5274133595 Combine like terms: -0.5274133595 + 0.5274133595 = 0.0000000000 0.0000000000 + x = -0.51259889 + 0.5274133595 x = -0.51259889 + 0.5274133595 Combine like terms: -0.51259889 + 0.5274133595 = 0.0148144695 x = 0.0148144695 Simplifying x = 0.0148144695Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.0400122495, 0.0148144695}
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