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Simplifying x2 + -28x + 7 = 0 Reorder the terms: 7 + -28x + x2 = 0 Solving 7 + -28x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-7' to each side of the equation. 7 + -28x + -7 + x2 = 0 + -7 Reorder the terms: 7 + -7 + -28x + x2 = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -28x + x2 = 0 + -7 -28x + x2 = 0 + -7 Combine like terms: 0 + -7 = -7 -28x + x2 = -7 The x term is -28x. Take half its coefficient (-14). Square it (196) and add it to both sides. Add '196' to each side of the equation. -28x + 196 + x2 = -7 + 196 Reorder the terms: 196 + -28x + x2 = -7 + 196 Combine like terms: -7 + 196 = 189 196 + -28x + x2 = 189 Factor a perfect square on the left side: (x + -14)(x + -14) = 189 Calculate the square root of the right side: 13.747727085 Break this problem into two subproblems by setting (x + -14) equal to 13.747727085 and -13.747727085.Subproblem 1
x + -14 = 13.747727085 Simplifying x + -14 = 13.747727085 Reorder the terms: -14 + x = 13.747727085 Solving -14 + x = 13.747727085 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '14' to each side of the equation. -14 + 14 + x = 13.747727085 + 14 Combine like terms: -14 + 14 = 0 0 + x = 13.747727085 + 14 x = 13.747727085 + 14 Combine like terms: 13.747727085 + 14 = 27.747727085 x = 27.747727085 Simplifying x = 27.747727085Subproblem 2
x + -14 = -13.747727085 Simplifying x + -14 = -13.747727085 Reorder the terms: -14 + x = -13.747727085 Solving -14 + x = -13.747727085 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '14' to each side of the equation. -14 + 14 + x = -13.747727085 + 14 Combine like terms: -14 + 14 = 0 0 + x = -13.747727085 + 14 x = -13.747727085 + 14 Combine like terms: -13.747727085 + 14 = 0.252272915 x = 0.252272915 Simplifying x = 0.252272915Solution
The solution to the problem is based on the solutions from the subproblems. x = {27.747727085, 0.252272915}
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