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Simplifying x2 + 2x + -248 = 0 Reorder the terms: -248 + 2x + x2 = 0 Solving -248 + 2x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '248' to each side of the equation. -248 + 2x + 248 + x2 = 0 + 248 Reorder the terms: -248 + 248 + 2x + x2 = 0 + 248 Combine like terms: -248 + 248 = 0 0 + 2x + x2 = 0 + 248 2x + x2 = 0 + 248 Combine like terms: 0 + 248 = 248 2x + x2 = 248 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 = 248 + 1 Reorder the terms: 1 + 2x + x2 = 248 + 1 Combine like terms: 248 + 1 = 249 1 + 2x + x2 = 249 Factor a perfect square on the left side: (x + 1)(x + 1) = 249 Calculate the square root of the right side: 15.779733838 Break this problem into two subproblems by setting (x + 1) equal to 15.779733838 and -15.779733838.Subproblem 1
x + 1 = 15.779733838 Simplifying x + 1 = 15.779733838 Reorder the terms: 1 + x = 15.779733838 Solving 1 + x = 15.779733838 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 = 15.779733838 + -1 Combine like terms: 1 + -1 = 0 0 + x = 15.779733838 + -1 x = 15.779733838 + -1 Combine like terms: 15.779733838 + -1 = 14.779733838 x = 14.779733838 Simplifying x = 14.779733838Subproblem 2
x + 1 = -15.779733838 Simplifying x + 1 = -15.779733838 Reorder the terms: 1 + x = -15.779733838 Solving 1 + x = -15.779733838 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 = -15.779733838 + -1 Combine like terms: 1 + -1 = 0 0 + x = -15.779733838 + -1 x = -15.779733838 + -1 Combine like terms: -15.779733838 + -1 = -16.779733838 x = -16.779733838 Simplifying x = -16.779733838Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.779733838, -16.779733838}
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