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Simplifying x2 + 2x + -1512 = 0 Reorder the terms: -1512 + 2x + x2 = 0 Solving -1512 + 2x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '1512' to each side of the equation. -1512 + 2x + 1512 + x2 = 0 + 1512 Reorder the terms: -1512 + 1512 + 2x + x2 = 0 + 1512 Combine like terms: -1512 + 1512 = 0 0 + 2x + x2 = 0 + 1512 2x + x2 = 0 + 1512 Combine like terms: 0 + 1512 = 1512 2x + x2 = 1512 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 = 1512 + 1 Reorder the terms: 1 + 2x + x2 = 1512 + 1 Combine like terms: 1512 + 1 = 1513 1 + 2x + x2 = 1513 Factor a perfect square on the left side: (x + 1)(x + 1) = 1513 Calculate the square root of the right side: 38.897300678 Break this problem into two subproblems by setting (x + 1) equal to 38.897300678 and -38.897300678.Subproblem 1
x + 1 = 38.897300678 Simplifying x + 1 = 38.897300678 Reorder the terms: 1 + x = 38.897300678 Solving 1 + x = 38.897300678 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 = 38.897300678 + -1 Combine like terms: 1 + -1 = 0 0 + x = 38.897300678 + -1 x = 38.897300678 + -1 Combine like terms: 38.897300678 + -1 = 37.897300678 x = 37.897300678 Simplifying x = 37.897300678Subproblem 2
x + 1 = -38.897300678 Simplifying x + 1 = -38.897300678 Reorder the terms: 1 + x = -38.897300678 Solving 1 + x = -38.897300678 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 = -38.897300678 + -1 Combine like terms: 1 + -1 = 0 0 + x = -38.897300678 + -1 x = -38.897300678 + -1 Combine like terms: -38.897300678 + -1 = -39.897300678 x = -39.897300678 Simplifying x = -39.897300678Solution
The solution to the problem is based on the solutions from the subproblems. x = {37.897300678, -39.897300678}
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