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Simplifying 22x2 + -2x + -16 = 0 Reorder the terms: -16 + -2x + 22x2 = 0 Solving -16 + -2x + 22x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-8 + -1x + 11x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-8 + -1x + 11x2)' equal to zero and attempt to solve: Simplifying -8 + -1x + 11x2 = 0 Solving -8 + -1x + 11x2 = 0 Begin completing the square. Divide all terms by 11 the coefficient of the squared term: Divide each side by '11'. -0.7272727273 + -0.09090909091x + x2 = 0 Move the constant term to the right: Add '0.7272727273' to each side of the equation. -0.7272727273 + -0.09090909091x + 0.7272727273 + x2 = 0 + 0.7272727273 Reorder the terms: -0.7272727273 + 0.7272727273 + -0.09090909091x + x2 = 0 + 0.7272727273 Combine like terms: -0.7272727273 + 0.7272727273 = 0.0000000000 0.0000000000 + -0.09090909091x + x2 = 0 + 0.7272727273 -0.09090909091x + x2 = 0 + 0.7272727273 Combine like terms: 0 + 0.7272727273 = 0.7272727273 -0.09090909091x + x2 = 0.7272727273 The x term is -0.09090909091x. Take half its coefficient (-0.04545454546). Square it (0.002066115703) and add it to both sides. Add '0.002066115703' to each side of the equation. -0.09090909091x + 0.002066115703 + x2 = 0.7272727273 + 0.002066115703 Reorder the terms: 0.002066115703 + -0.09090909091x + x2 = 0.7272727273 + 0.002066115703 Combine like terms: 0.7272727273 + 0.002066115703 = 0.729338843003 0.002066115703 + -0.09090909091x + x2 = 0.729338843003 Factor a perfect square on the left side: (x + -0.04545454546)(x + -0.04545454546) = 0.729338843003 Calculate the square root of the right side: 0.854013374 Break this problem into two subproblems by setting (x + -0.04545454546) equal to 0.854013374 and -0.854013374.Subproblem 1
x + -0.04545454546 = 0.854013374 Simplifying x + -0.04545454546 = 0.854013374 Reorder the terms: -0.04545454546 + x = 0.854013374 Solving -0.04545454546 + x = 0.854013374 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.04545454546' to each side of the equation. -0.04545454546 + 0.04545454546 + x = 0.854013374 + 0.04545454546 Combine like terms: -0.04545454546 + 0.04545454546 = 0.00000000000 0.00000000000 + x = 0.854013374 + 0.04545454546 x = 0.854013374 + 0.04545454546 Combine like terms: 0.854013374 + 0.04545454546 = 0.89946791946 x = 0.89946791946 Simplifying x = 0.89946791946Subproblem 2
x + -0.04545454546 = -0.854013374 Simplifying x + -0.04545454546 = -0.854013374 Reorder the terms: -0.04545454546 + x = -0.854013374 Solving -0.04545454546 + x = -0.854013374 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.04545454546' to each side of the equation. -0.04545454546 + 0.04545454546 + x = -0.854013374 + 0.04545454546 Combine like terms: -0.04545454546 + 0.04545454546 = 0.00000000000 0.00000000000 + x = -0.854013374 + 0.04545454546 x = -0.854013374 + 0.04545454546 Combine like terms: -0.854013374 + 0.04545454546 = -0.80855882854 x = -0.80855882854 Simplifying x = -0.80855882854Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.89946791946, -0.80855882854}Solution
x = {0.89946791946, -0.80855882854}
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