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Simplifying 22x2 + -28x + 4 = 0 Reorder the terms: 4 + -28x + 22x2 = 0 Solving 4 + -28x + 22x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(2 + -14x + 11x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(2 + -14x + 11x2)' equal to zero and attempt to solve: Simplifying 2 + -14x + 11x2 = 0 Solving 2 + -14x + 11x2 = 0 Begin completing the square. Divide all terms by 11 the coefficient of the squared term: Divide each side by '11'. 0.1818181818 + -1.272727273x + x2 = 0 Move the constant term to the right: Add '-0.1818181818' to each side of the equation. 0.1818181818 + -1.272727273x + -0.1818181818 + x2 = 0 + -0.1818181818 Reorder the terms: 0.1818181818 + -0.1818181818 + -1.272727273x + x2 = 0 + -0.1818181818 Combine like terms: 0.1818181818 + -0.1818181818 = 0.0000000000 0.0000000000 + -1.272727273x + x2 = 0 + -0.1818181818 -1.272727273x + x2 = 0 + -0.1818181818 Combine like terms: 0 + -0.1818181818 = -0.1818181818 -1.272727273x + x2 = -0.1818181818 The x term is -1.272727273x. Take half its coefficient (-0.6363636365). Square it (0.4049586779) and add it to both sides. Add '0.4049586779' to each side of the equation. -1.272727273x + 0.4049586779 + x2 = -0.1818181818 + 0.4049586779 Reorder the terms: 0.4049586779 + -1.272727273x + x2 = -0.1818181818 + 0.4049586779 Combine like terms: -0.1818181818 + 0.4049586779 = 0.2231404961 0.4049586779 + -1.272727273x + x2 = 0.2231404961 Factor a perfect square on the left side: (x + -0.6363636365)(x + -0.6363636365) = 0.2231404961 Calculate the square root of the right side: 0.472377493 Break this problem into two subproblems by setting (x + -0.6363636365) equal to 0.472377493 and -0.472377493.Subproblem 1
x + -0.6363636365 = 0.472377493 Simplifying x + -0.6363636365 = 0.472377493 Reorder the terms: -0.6363636365 + x = 0.472377493 Solving -0.6363636365 + x = 0.472377493 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.6363636365' to each side of the equation. -0.6363636365 + 0.6363636365 + x = 0.472377493 + 0.6363636365 Combine like terms: -0.6363636365 + 0.6363636365 = 0.0000000000 0.0000000000 + x = 0.472377493 + 0.6363636365 x = 0.472377493 + 0.6363636365 Combine like terms: 0.472377493 + 0.6363636365 = 1.1087411295 x = 1.1087411295 Simplifying x = 1.1087411295Subproblem 2
x + -0.6363636365 = -0.472377493 Simplifying x + -0.6363636365 = -0.472377493 Reorder the terms: -0.6363636365 + x = -0.472377493 Solving -0.6363636365 + x = -0.472377493 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.6363636365' to each side of the equation. -0.6363636365 + 0.6363636365 + x = -0.472377493 + 0.6363636365 Combine like terms: -0.6363636365 + 0.6363636365 = 0.0000000000 0.0000000000 + x = -0.472377493 + 0.6363636365 x = -0.472377493 + 0.6363636365 Combine like terms: -0.472377493 + 0.6363636365 = 0.1639861435 x = 0.1639861435 Simplifying x = 0.1639861435Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.1087411295, 0.1639861435}Solution
x = {1.1087411295, 0.1639861435}
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