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Simplifying 22x2 + 20x + 4 = 0 Reorder the terms: 4 + 20x + 22x2 = 0 Solving 4 + 20x + 22x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(2 + 10x + 11x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(2 + 10x + 11x2)' equal to zero and attempt to solve: Simplifying 2 + 10x + 11x2 = 0 Solving 2 + 10x + 11x2 = 0 Begin completing the square. Divide all terms by 11 the coefficient of the squared term: Divide each side by '11'. 0.1818181818 + 0.9090909091x + x2 = 0 Move the constant term to the right: Add '-0.1818181818' to each side of the equation. 0.1818181818 + 0.9090909091x + -0.1818181818 + x2 = 0 + -0.1818181818 Reorder the terms: 0.1818181818 + -0.1818181818 + 0.9090909091x + x2 = 0 + -0.1818181818 Combine like terms: 0.1818181818 + -0.1818181818 = 0.0000000000 0.0000000000 + 0.9090909091x + x2 = 0 + -0.1818181818 0.9090909091x + x2 = 0 + -0.1818181818 Combine like terms: 0 + -0.1818181818 = -0.1818181818 0.9090909091x + x2 = -0.1818181818 The x term is 0.9090909091x. Take half its coefficient (0.4545454546). Square it (0.2066115703) and add it to both sides. Add '0.2066115703' to each side of the equation. 0.9090909091x + 0.2066115703 + x2 = -0.1818181818 + 0.2066115703 Reorder the terms: 0.2066115703 + 0.9090909091x + x2 = -0.1818181818 + 0.2066115703 Combine like terms: -0.1818181818 + 0.2066115703 = 0.0247933885 0.2066115703 + 0.9090909091x + x2 = 0.0247933885 Factor a perfect square on the left side: (x + 0.4545454546)(x + 0.4545454546) = 0.0247933885 Calculate the square root of the right side: 0.157459165 Break this problem into two subproblems by setting (x + 0.4545454546) equal to 0.157459165 and -0.157459165.Subproblem 1
x + 0.4545454546 = 0.157459165 Simplifying x + 0.4545454546 = 0.157459165 Reorder the terms: 0.4545454546 + x = 0.157459165 Solving 0.4545454546 + x = 0.157459165 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4545454546' to each side of the equation. 0.4545454546 + -0.4545454546 + x = 0.157459165 + -0.4545454546 Combine like terms: 0.4545454546 + -0.4545454546 = 0.0000000000 0.0000000000 + x = 0.157459165 + -0.4545454546 x = 0.157459165 + -0.4545454546 Combine like terms: 0.157459165 + -0.4545454546 = -0.2970862896 x = -0.2970862896 Simplifying x = -0.2970862896Subproblem 2
x + 0.4545454546 = -0.157459165 Simplifying x + 0.4545454546 = -0.157459165 Reorder the terms: 0.4545454546 + x = -0.157459165 Solving 0.4545454546 + x = -0.157459165 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4545454546' to each side of the equation. 0.4545454546 + -0.4545454546 + x = -0.157459165 + -0.4545454546 Combine like terms: 0.4545454546 + -0.4545454546 = 0.0000000000 0.0000000000 + x = -0.157459165 + -0.4545454546 x = -0.157459165 + -0.4545454546 Combine like terms: -0.157459165 + -0.4545454546 = -0.6120046196 x = -0.6120046196 Simplifying x = -0.6120046196Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.2970862896, -0.6120046196}Solution
x = {-0.2970862896, -0.6120046196}
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