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Simplifying x2 + -14x + -49 + x2 = x2 + 14x + 49 Reorder the terms: -49 + -14x + x2 + x2 = x2 + 14x + 49 Combine like terms: x2 + x2 = 2x2 -49 + -14x + 2x2 = x2 + 14x + 49 Reorder the terms: -49 + -14x + 2x2 = 49 + 14x + x2 Solving -49 + -14x + 2x2 = 49 + 14x + x2 Solving for variable 'x'. Reorder the terms: -49 + -49 + -14x + -14x + 2x2 + -1x2 = 49 + 14x + x2 + -49 + -14x + -1x2 Combine like terms: -49 + -49 = -98 -98 + -14x + -14x + 2x2 + -1x2 = 49 + 14x + x2 + -49 + -14x + -1x2 Combine like terms: -14x + -14x = -28x -98 + -28x + 2x2 + -1x2 = 49 + 14x + x2 + -49 + -14x + -1x2 Combine like terms: 2x2 + -1x2 = 1x2 -98 + -28x + 1x2 = 49 + 14x + x2 + -49 + -14x + -1x2 Reorder the terms: -98 + -28x + 1x2 = 49 + -49 + 14x + -14x + x2 + -1x2 Combine like terms: 49 + -49 = 0 -98 + -28x + 1x2 = 0 + 14x + -14x + x2 + -1x2 -98 + -28x + 1x2 = 14x + -14x + x2 + -1x2 Combine like terms: 14x + -14x = 0 -98 + -28x + 1x2 = 0 + x2 + -1x2 -98 + -28x + 1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -98 + -28x + 1x2 = 0 Begin completing the square. Move the constant term to the right: Add '98' to each side of the equation. -98 + -28x + 98 + x2 = 0 + 98 Reorder the terms: -98 + 98 + -28x + x2 = 0 + 98 Combine like terms: -98 + 98 = 0 0 + -28x + x2 = 0 + 98 -28x + x2 = 0 + 98 Combine like terms: 0 + 98 = 98 -28x + x2 = 98 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 = 98 + 196 Reorder the terms: 196 + -28x + x2 = 98 + 196 Combine like terms: 98 + 196 = 294 196 + -28x + x2 = 294 Factor a perfect square on the left side: (x + -14)(x + -14) = 294 Calculate the square root of the right side: 17.146428199 Break this problem into two subproblems by setting (x + -14) equal to 17.146428199 and -17.146428199.Subproblem 1
x + -14 = 17.146428199 Simplifying x + -14 = 17.146428199 Reorder the terms: -14 + x = 17.146428199 Solving -14 + x = 17.146428199 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 = 17.146428199 + 14 Combine like terms: -14 + 14 = 0 0 + x = 17.146428199 + 14 x = 17.146428199 + 14 Combine like terms: 17.146428199 + 14 = 31.146428199 x = 31.146428199 Simplifying x = 31.146428199Subproblem 2
x + -14 = -17.146428199 Simplifying x + -14 = -17.146428199 Reorder the terms: -14 + x = -17.146428199 Solving -14 + x = -17.146428199 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 = -17.146428199 + 14 Combine like terms: -14 + 14 = 0 0 + x = -17.146428199 + 14 x = -17.146428199 + 14 Combine like terms: -17.146428199 + 14 = -3.146428199 x = -3.146428199 Simplifying x = -3.146428199Solution
The solution to the problem is based on the solutions from the subproblems. x = {31.146428199, -3.146428199}
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