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Simplifying x2 + 2x + -15.21 = 0 Reorder the terms: -15.21 + 2x + x2 = 0 Solving -15.21 + 2x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '15.21' to each side of the equation. -15.21 + 2x + 15.21 + x2 = 0 + 15.21 Reorder the terms: -15.21 + 15.21 + 2x + x2 = 0 + 15.21 Combine like terms: -15.21 + 15.21 = 0.00 0.00 + 2x + x2 = 0 + 15.21 2x + x2 = 0 + 15.21 Combine like terms: 0 + 15.21 = 15.21 2x + x2 = 15.21 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 = 15.21 + 1 Reorder the terms: 1 + 2x + x2 = 15.21 + 1 Combine like terms: 15.21 + 1 = 16.21 1 + 2x + x2 = 16.21 Factor a perfect square on the left side: (x + 1)(x + 1) = 16.21 Calculate the square root of the right side: 4.026164428 Break this problem into two subproblems by setting (x + 1) equal to 4.026164428 and -4.026164428.Subproblem 1
x + 1 = 4.026164428 Simplifying x + 1 = 4.026164428 Reorder the terms: 1 + x = 4.026164428 Solving 1 + x = 4.026164428 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 = 4.026164428 + -1 Combine like terms: 1 + -1 = 0 0 + x = 4.026164428 + -1 x = 4.026164428 + -1 Combine like terms: 4.026164428 + -1 = 3.026164428 x = 3.026164428 Simplifying x = 3.026164428Subproblem 2
x + 1 = -4.026164428 Simplifying x + 1 = -4.026164428 Reorder the terms: 1 + x = -4.026164428 Solving 1 + x = -4.026164428 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 = -4.026164428 + -1 Combine like terms: 1 + -1 = 0 0 + x = -4.026164428 + -1 x = -4.026164428 + -1 Combine like terms: -4.026164428 + -1 = -5.026164428 x = -5.026164428 Simplifying x = -5.026164428Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.026164428, -5.026164428}
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