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Simplifying 6x = 22x2 + 11x + 1 Reorder the terms: 6x = 1 + 11x + 22x2 Solving 6x = 1 + 11x + 22x2 Solving for variable 'x'. Reorder the terms: -1 + 6x + -11x + -22x2 = 1 + 11x + 22x2 + -1 + -11x + -22x2 Combine like terms: 6x + -11x = -5x -1 + -5x + -22x2 = 1 + 11x + 22x2 + -1 + -11x + -22x2 Reorder the terms: -1 + -5x + -22x2 = 1 + -1 + 11x + -11x + 22x2 + -22x2 Combine like terms: 1 + -1 = 0 -1 + -5x + -22x2 = 0 + 11x + -11x + 22x2 + -22x2 -1 + -5x + -22x2 = 11x + -11x + 22x2 + -22x2 Combine like terms: 11x + -11x = 0 -1 + -5x + -22x2 = 0 + 22x2 + -22x2 -1 + -5x + -22x2 = 22x2 + -22x2 Combine like terms: 22x2 + -22x2 = 0 -1 + -5x + -22x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(1 + 5x + 22x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(1 + 5x + 22x2)' equal to zero and attempt to solve: Simplifying 1 + 5x + 22x2 = 0 Solving 1 + 5x + 22x2 = 0 Begin completing the square. Divide all terms by 22 the coefficient of the squared term: Divide each side by '22'. 0.04545454545 + 0.2272727273x + x2 = 0 Move the constant term to the right: Add '-0.04545454545' to each side of the equation. 0.04545454545 + 0.2272727273x + -0.04545454545 + x2 = 0 + -0.04545454545 Reorder the terms: 0.04545454545 + -0.04545454545 + 0.2272727273x + x2 = 0 + -0.04545454545 Combine like terms: 0.04545454545 + -0.04545454545 = 0.00000000000 0.00000000000 + 0.2272727273x + x2 = 0 + -0.04545454545 0.2272727273x + x2 = 0 + -0.04545454545 Combine like terms: 0 + -0.04545454545 = -0.04545454545 0.2272727273x + x2 = -0.04545454545 The x term is 0.2272727273x. Take half its coefficient (0.1136363637). Square it (0.01291322316) and add it to both sides. Add '0.01291322316' to each side of the equation. 0.2272727273x + 0.01291322316 + x2 = -0.04545454545 + 0.01291322316 Reorder the terms: 0.01291322316 + 0.2272727273x + x2 = -0.04545454545 + 0.01291322316 Combine like terms: -0.04545454545 + 0.01291322316 = -0.03254132229 0.01291322316 + 0.2272727273x + x2 = -0.03254132229 Factor a perfect square on the left side: (x + 0.1136363637)(x + 0.1136363637) = -0.03254132229 Can't calculate square root of the right side. The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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