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Simplifying x2 + 2x + -1290 = 0 Reorder the terms: -1290 + 2x + x2 = 0 Solving -1290 + 2x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '1290' to each side of the equation. -1290 + 2x + 1290 + x2 = 0 + 1290 Reorder the terms: -1290 + 1290 + 2x + x2 = 0 + 1290 Combine like terms: -1290 + 1290 = 0 0 + 2x + x2 = 0 + 1290 2x + x2 = 0 + 1290 Combine like terms: 0 + 1290 = 1290 2x + x2 = 1290 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 = 1290 + 1 Reorder the terms: 1 + 2x + x2 = 1290 + 1 Combine like terms: 1290 + 1 = 1291 1 + 2x + x2 = 1291 Factor a perfect square on the left side: (x + 1)(x + 1) = 1291 Calculate the square root of the right side: 35.930488446 Break this problem into two subproblems by setting (x + 1) equal to 35.930488446 and -35.930488446.Subproblem 1
x + 1 = 35.930488446 Simplifying x + 1 = 35.930488446 Reorder the terms: 1 + x = 35.930488446 Solving 1 + x = 35.930488446 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 = 35.930488446 + -1 Combine like terms: 1 + -1 = 0 0 + x = 35.930488446 + -1 x = 35.930488446 + -1 Combine like terms: 35.930488446 + -1 = 34.930488446 x = 34.930488446 Simplifying x = 34.930488446Subproblem 2
x + 1 = -35.930488446 Simplifying x + 1 = -35.930488446 Reorder the terms: 1 + x = -35.930488446 Solving 1 + x = -35.930488446 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 = -35.930488446 + -1 Combine like terms: 1 + -1 = 0 0 + x = -35.930488446 + -1 x = -35.930488446 + -1 Combine like terms: -35.930488446 + -1 = -36.930488446 x = -36.930488446 Simplifying x = -36.930488446Solution
The solution to the problem is based on the solutions from the subproblems. x = {34.930488446, -36.930488446}
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