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Simplifying x2 + -28x + 14 = 0 Reorder the terms: 14 + -28x + x2 = 0 Solving 14 + -28x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-14' to each side of the equation. 14 + -28x + -14 + x2 = 0 + -14 Reorder the terms: 14 + -14 + -28x + x2 = 0 + -14 Combine like terms: 14 + -14 = 0 0 + -28x + x2 = 0 + -14 -28x + x2 = 0 + -14 Combine like terms: 0 + -14 = -14 -28x + x2 = -14 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 = -14 + 196 Reorder the terms: 196 + -28x + x2 = -14 + 196 Combine like terms: -14 + 196 = 182 196 + -28x + x2 = 182 Factor a perfect square on the left side: (x + -14)(x + -14) = 182 Calculate the square root of the right side: 13.490737563 Break this problem into two subproblems by setting (x + -14) equal to 13.490737563 and -13.490737563.Subproblem 1
x + -14 = 13.490737563 Simplifying x + -14 = 13.490737563 Reorder the terms: -14 + x = 13.490737563 Solving -14 + x = 13.490737563 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 = 13.490737563 + 14 Combine like terms: -14 + 14 = 0 0 + x = 13.490737563 + 14 x = 13.490737563 + 14 Combine like terms: 13.490737563 + 14 = 27.490737563 x = 27.490737563 Simplifying x = 27.490737563Subproblem 2
x + -14 = -13.490737563 Simplifying x + -14 = -13.490737563 Reorder the terms: -14 + x = -13.490737563 Solving -14 + x = -13.490737563 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 = -13.490737563 + 14 Combine like terms: -14 + 14 = 0 0 + x = -13.490737563 + 14 x = -13.490737563 + 14 Combine like terms: -13.490737563 + 14 = 0.509262437 x = 0.509262437 Simplifying x = 0.509262437Solution
The solution to the problem is based on the solutions from the subproblems. x = {27.490737563, 0.509262437}
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