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Simplifying x2 + 2x = 27.5 Reorder the terms: 2x + x2 = 27.5 Solving 2x + x2 = 27.5 Solving for variable 'x'. Reorder the terms: -27.5 + 2x + x2 = 27.5 + -27.5 Combine like terms: 27.5 + -27.5 = 0.0 -27.5 + 2x + x2 = 0.0 Begin completing the square. Move the constant term to the right: Add '27.5' to each side of the equation. -27.5 + 2x + 27.5 + x2 = 0.0 + 27.5 Reorder the terms: -27.5 + 27.5 + 2x + x2 = 0.0 + 27.5 Combine like terms: -27.5 + 27.5 = 0.0 0.0 + 2x + x2 = 0.0 + 27.5 2x + x2 = 0.0 + 27.5 Combine like terms: 0.0 + 27.5 = 27.5 2x + x2 = 27.5 The x term is 2x. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x + 1 + x2 = 27.5 + 1 Reorder the terms: 1 + 2x + x2 = 27.5 + 1 Combine like terms: 27.5 + 1 = 28.5 1 + 2x + x2 = 28.5 Factor a perfect square on the left side: (x + 1)(x + 1) = 28.5 Calculate the square root of the right side: 5.338539126 Break this problem into two subproblems by setting (x + 1) equal to 5.338539126 and -5.338539126.Subproblem 1
x + 1 = 5.338539126 Simplifying x + 1 = 5.338539126 Reorder the terms: 1 + x = 5.338539126 Solving 1 + x = 5.338539126 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 5.338539126 + -1 Combine like terms: 1 + -1 = 0 0 + x = 5.338539126 + -1 x = 5.338539126 + -1 Combine like terms: 5.338539126 + -1 = 4.338539126 x = 4.338539126 Simplifying x = 4.338539126Subproblem 2
x + 1 = -5.338539126 Simplifying x + 1 = -5.338539126 Reorder the terms: 1 + x = -5.338539126 Solving 1 + x = -5.338539126 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -5.338539126 + -1 Combine like terms: 1 + -1 = 0 0 + x = -5.338539126 + -1 x = -5.338539126 + -1 Combine like terms: -5.338539126 + -1 = -6.338539126 x = -6.338539126 Simplifying x = -6.338539126Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.338539126, -6.338539126}
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