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Simplifying 2x2 + -28x + -2 = 50 Reorder the terms: -2 + -28x + 2x2 = 50 Solving -2 + -28x + 2x2 = 50 Solving for variable 'x'. Reorder the terms: -2 + -50 + -28x + 2x2 = 50 + -50 Combine like terms: -2 + -50 = -52 -52 + -28x + 2x2 = 50 + -50 Combine like terms: 50 + -50 = 0 -52 + -28x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-26 + -14x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-26 + -14x + x2)' equal to zero and attempt to solve: Simplifying -26 + -14x + x2 = 0 Solving -26 + -14x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '26' to each side of the equation. -26 + -14x + 26 + x2 = 0 + 26 Reorder the terms: -26 + 26 + -14x + x2 = 0 + 26 Combine like terms: -26 + 26 = 0 0 + -14x + x2 = 0 + 26 -14x + x2 = 0 + 26 Combine like terms: 0 + 26 = 26 -14x + x2 = 26 The x term is -14x. Take half its coefficient (-7). Square it (49) and add it to both sides. Add '49' to each side of the equation. -14x + 49 + x2 = 26 + 49 Reorder the terms: 49 + -14x + x2 = 26 + 49 Combine like terms: 26 + 49 = 75 49 + -14x + x2 = 75 Factor a perfect square on the left side: (x + -7)(x + -7) = 75 Calculate the square root of the right side: 8.660254038 Break this problem into two subproblems by setting (x + -7) equal to 8.660254038 and -8.660254038.Subproblem 1
x + -7 = 8.660254038 Simplifying x + -7 = 8.660254038 Reorder the terms: -7 + x = 8.660254038 Solving -7 + x = 8.660254038 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + x = 8.660254038 + 7 Combine like terms: -7 + 7 = 0 0 + x = 8.660254038 + 7 x = 8.660254038 + 7 Combine like terms: 8.660254038 + 7 = 15.660254038 x = 15.660254038 Simplifying x = 15.660254038Subproblem 2
x + -7 = -8.660254038 Simplifying x + -7 = -8.660254038 Reorder the terms: -7 + x = -8.660254038 Solving -7 + x = -8.660254038 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + x = -8.660254038 + 7 Combine like terms: -7 + 7 = 0 0 + x = -8.660254038 + 7 x = -8.660254038 + 7 Combine like terms: -8.660254038 + 7 = -1.660254038 x = -1.660254038 Simplifying x = -1.660254038Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.660254038, -1.660254038}Solution
x = {15.660254038, -1.660254038}
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