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Simplifying 28x2 + -12x + 1 = 0 Reorder the terms: 1 + -12x + 28x2 = 0 Solving 1 + -12x + 28x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 28 the coefficient of the squared term: Divide each side by '28'. 0.03571428571 + -0.4285714286x + x2 = 0 Move the constant term to the right: Add '-0.03571428571' to each side of the equation. 0.03571428571 + -0.4285714286x + -0.03571428571 + x2 = 0 + -0.03571428571 Reorder the terms: 0.03571428571 + -0.03571428571 + -0.4285714286x + x2 = 0 + -0.03571428571 Combine like terms: 0.03571428571 + -0.03571428571 = 0.00000000000 0.00000000000 + -0.4285714286x + x2 = 0 + -0.03571428571 -0.4285714286x + x2 = 0 + -0.03571428571 Combine like terms: 0 + -0.03571428571 = -0.03571428571 -0.4285714286x + x2 = -0.03571428571 The x term is -0.4285714286x. Take half its coefficient (-0.2142857143). Square it (0.04591836735) and add it to both sides. Add '0.04591836735' to each side of the equation. -0.4285714286x + 0.04591836735 + x2 = -0.03571428571 + 0.04591836735 Reorder the terms: 0.04591836735 + -0.4285714286x + x2 = -0.03571428571 + 0.04591836735 Combine like terms: -0.03571428571 + 0.04591836735 = 0.01020408164 0.04591836735 + -0.4285714286x + x2 = 0.01020408164 Factor a perfect square on the left side: (x + -0.2142857143)(x + -0.2142857143) = 0.01020408164 Calculate the square root of the right side: 0.101015254 Break this problem into two subproblems by setting (x + -0.2142857143) equal to 0.101015254 and -0.101015254.Subproblem 1
x + -0.2142857143 = 0.101015254 Simplifying x + -0.2142857143 = 0.101015254 Reorder the terms: -0.2142857143 + x = 0.101015254 Solving -0.2142857143 + x = 0.101015254 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2142857143' to each side of the equation. -0.2142857143 + 0.2142857143 + x = 0.101015254 + 0.2142857143 Combine like terms: -0.2142857143 + 0.2142857143 = 0.0000000000 0.0000000000 + x = 0.101015254 + 0.2142857143 x = 0.101015254 + 0.2142857143 Combine like terms: 0.101015254 + 0.2142857143 = 0.3153009683 x = 0.3153009683 Simplifying x = 0.3153009683Subproblem 2
x + -0.2142857143 = -0.101015254 Simplifying x + -0.2142857143 = -0.101015254 Reorder the terms: -0.2142857143 + x = -0.101015254 Solving -0.2142857143 + x = -0.101015254 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2142857143' to each side of the equation. -0.2142857143 + 0.2142857143 + x = -0.101015254 + 0.2142857143 Combine like terms: -0.2142857143 + 0.2142857143 = 0.0000000000 0.0000000000 + x = -0.101015254 + 0.2142857143 x = -0.101015254 + 0.2142857143 Combine like terms: -0.101015254 + 0.2142857143 = 0.1132704603 x = 0.1132704603 Simplifying x = 0.1132704603Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.3153009683, 0.1132704603}
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