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Simplifying x2 + -28x = -11 Reorder the terms: -28x + x2 = -11 Solving -28x + x2 = -11 Solving for variable 'x'. Reorder the terms: 11 + -28x + x2 = -11 + 11 Combine like terms: -11 + 11 = 0 11 + -28x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-11' to each side of the equation. 11 + -28x + -11 + x2 = 0 + -11 Reorder the terms: 11 + -11 + -28x + x2 = 0 + -11 Combine like terms: 11 + -11 = 0 0 + -28x + x2 = 0 + -11 -28x + x2 = 0 + -11 Combine like terms: 0 + -11 = -11 -28x + x2 = -11 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 = -11 + 196 Reorder the terms: 196 + -28x + x2 = -11 + 196 Combine like terms: -11 + 196 = 185 196 + -28x + x2 = 185 Factor a perfect square on the left side: (x + -14)(x + -14) = 185 Calculate the square root of the right side: 13.601470509 Break this problem into two subproblems by setting (x + -14) equal to 13.601470509 and -13.601470509.Subproblem 1
x + -14 = 13.601470509 Simplifying x + -14 = 13.601470509 Reorder the terms: -14 + x = 13.601470509 Solving -14 + x = 13.601470509 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 = 13.601470509 + 14 Combine like terms: -14 + 14 = 0 0 + x = 13.601470509 + 14 x = 13.601470509 + 14 Combine like terms: 13.601470509 + 14 = 27.601470509 x = 27.601470509 Simplifying x = 27.601470509Subproblem 2
x + -14 = -13.601470509 Simplifying x + -14 = -13.601470509 Reorder the terms: -14 + x = -13.601470509 Solving -14 + x = -13.601470509 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 = -13.601470509 + 14 Combine like terms: -14 + 14 = 0 0 + x = -13.601470509 + 14 x = -13.601470509 + 14 Combine like terms: -13.601470509 + 14 = 0.398529491 x = 0.398529491 Simplifying x = 0.398529491Solution
The solution to the problem is based on the solutions from the subproblems. x = {27.601470509, 0.398529491}
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