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Simplifying 28x2 + -114x + 36 = 0 Reorder the terms: 36 + -114x + 28x2 = 0 Solving 36 + -114x + 28x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(18 + -57x + 14x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(18 + -57x + 14x2)' equal to zero and attempt to solve: Simplifying 18 + -57x + 14x2 = 0 Solving 18 + -57x + 14x2 = 0 Begin completing the square. Divide all terms by 14 the coefficient of the squared term: Divide each side by '14'. 1.285714286 + -4.071428571x + x2 = 0 Move the constant term to the right: Add '-1.285714286' to each side of the equation. 1.285714286 + -4.071428571x + -1.285714286 + x2 = 0 + -1.285714286 Reorder the terms: 1.285714286 + -1.285714286 + -4.071428571x + x2 = 0 + -1.285714286 Combine like terms: 1.285714286 + -1.285714286 = 0.000000000 0.000000000 + -4.071428571x + x2 = 0 + -1.285714286 -4.071428571x + x2 = 0 + -1.285714286 Combine like terms: 0 + -1.285714286 = -1.285714286 -4.071428571x + x2 = -1.285714286 The x term is -4.071428571x. Take half its coefficient (-2.035714286). Square it (4.144132654) and add it to both sides. Add '4.144132654' to each side of the equation. -4.071428571x + 4.144132654 + x2 = -1.285714286 + 4.144132654 Reorder the terms: 4.144132654 + -4.071428571x + x2 = -1.285714286 + 4.144132654 Combine like terms: -1.285714286 + 4.144132654 = 2.858418368 4.144132654 + -4.071428571x + x2 = 2.858418368 Factor a perfect square on the left side: (x + -2.035714286)(x + -2.035714286) = 2.858418368 Calculate the square root of the right side: 1.690685769 Break this problem into two subproblems by setting (x + -2.035714286) equal to 1.690685769 and -1.690685769.Subproblem 1
x + -2.035714286 = 1.690685769 Simplifying x + -2.035714286 = 1.690685769 Reorder the terms: -2.035714286 + x = 1.690685769 Solving -2.035714286 + x = 1.690685769 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.035714286' to each side of the equation. -2.035714286 + 2.035714286 + x = 1.690685769 + 2.035714286 Combine like terms: -2.035714286 + 2.035714286 = 0.000000000 0.000000000 + x = 1.690685769 + 2.035714286 x = 1.690685769 + 2.035714286 Combine like terms: 1.690685769 + 2.035714286 = 3.726400055 x = 3.726400055 Simplifying x = 3.726400055Subproblem 2
x + -2.035714286 = -1.690685769 Simplifying x + -2.035714286 = -1.690685769 Reorder the terms: -2.035714286 + x = -1.690685769 Solving -2.035714286 + x = -1.690685769 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.035714286' to each side of the equation. -2.035714286 + 2.035714286 + x = -1.690685769 + 2.035714286 Combine like terms: -2.035714286 + 2.035714286 = 0.000000000 0.000000000 + x = -1.690685769 + 2.035714286 x = -1.690685769 + 2.035714286 Combine like terms: -1.690685769 + 2.035714286 = 0.345028517 x = 0.345028517 Simplifying x = 0.345028517Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.726400055, 0.345028517}Solution
x = {3.726400055, 0.345028517}
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