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Simplifying X2 + 2X + -35.25 = 0 Reorder the terms: -35.25 + 2X + X2 = 0 Solving -35.25 + 2X + X2 = 0 Solving for variable 'X'. Begin completing the square. Move the constant term to the right: Add '35.25' to each side of the equation. -35.25 + 2X + 35.25 + X2 = 0 + 35.25 Reorder the terms: -35.25 + 35.25 + 2X + X2 = 0 + 35.25 Combine like terms: -35.25 + 35.25 = 0.00 0.00 + 2X + X2 = 0 + 35.25 2X + X2 = 0 + 35.25 Combine like terms: 0 + 35.25 = 35.25 2X + X2 = 35.25 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 = 35.25 + 1 Reorder the terms: 1 + 2X + X2 = 35.25 + 1 Combine like terms: 35.25 + 1 = 36.25 1 + 2X + X2 = 36.25 Factor a perfect square on the left side: (X + 1)(X + 1) = 36.25 Calculate the square root of the right side: 6.020797289 Break this problem into two subproblems by setting (X + 1) equal to 6.020797289 and -6.020797289.Subproblem 1
X + 1 = 6.020797289 Simplifying X + 1 = 6.020797289 Reorder the terms: 1 + X = 6.020797289 Solving 1 + X = 6.020797289 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 = 6.020797289 + -1 Combine like terms: 1 + -1 = 0 0 + X = 6.020797289 + -1 X = 6.020797289 + -1 Combine like terms: 6.020797289 + -1 = 5.020797289 X = 5.020797289 Simplifying X = 5.020797289Subproblem 2
X + 1 = -6.020797289 Simplifying X + 1 = -6.020797289 Reorder the terms: 1 + X = -6.020797289 Solving 1 + X = -6.020797289 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 = -6.020797289 + -1 Combine like terms: 1 + -1 = 0 0 + X = -6.020797289 + -1 X = -6.020797289 + -1 Combine like terms: -6.020797289 + -1 = -7.020797289 X = -7.020797289 Simplifying X = -7.020797289Solution
The solution to the problem is based on the solutions from the subproblems. X = {5.020797289, -7.020797289}
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