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Simplifying x2 + 2x + -2.75 = 0 Reorder the terms: -2.75 + 2x + x2 = 0 Solving -2.75 + 2x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '2.75' to each side of the equation. -2.75 + 2x + 2.75 + x2 = 0 + 2.75 Reorder the terms: -2.75 + 2.75 + 2x + x2 = 0 + 2.75 Combine like terms: -2.75 + 2.75 = 0.00 0.00 + 2x + x2 = 0 + 2.75 2x + x2 = 0 + 2.75 Combine like terms: 0 + 2.75 = 2.75 2x + x2 = 2.75 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 = 2.75 + 1 Reorder the terms: 1 + 2x + x2 = 2.75 + 1 Combine like terms: 2.75 + 1 = 3.75 1 + 2x + x2 = 3.75 Factor a perfect square on the left side: (x + 1)(x + 1) = 3.75 Calculate the square root of the right side: 1.936491673 Break this problem into two subproblems by setting (x + 1) equal to 1.936491673 and -1.936491673.Subproblem 1
x + 1 = 1.936491673 Simplifying x + 1 = 1.936491673 Reorder the terms: 1 + x = 1.936491673 Solving 1 + x = 1.936491673 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 = 1.936491673 + -1 Combine like terms: 1 + -1 = 0 0 + x = 1.936491673 + -1 x = 1.936491673 + -1 Combine like terms: 1.936491673 + -1 = 0.936491673 x = 0.936491673 Simplifying x = 0.936491673Subproblem 2
x + 1 = -1.936491673 Simplifying x + 1 = -1.936491673 Reorder the terms: 1 + x = -1.936491673 Solving 1 + x = -1.936491673 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 = -1.936491673 + -1 Combine like terms: 1 + -1 = 0 0 + x = -1.936491673 + -1 x = -1.936491673 + -1 Combine like terms: -1.936491673 + -1 = -2.936491673 x = -2.936491673 Simplifying x = -2.936491673Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.936491673, -2.936491673}
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