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Simplifying X2 + 2X + 1 = 10 Reorder the terms: 1 + 2X + X2 = 10 Solving 1 + 2X + X2 = 10 Solving for variable 'X'. Reorder the terms: 1 + -10 + 2X + X2 = 10 + -10 Combine like terms: 1 + -10 = -9 -9 + 2X + X2 = 10 + -10 Combine like terms: 10 + -10 = 0 -9 + 2X + X2 = 0 Begin completing the square. Move the constant term to the right: Add '9' to each side of the equation. -9 + 2X + 9 + X2 = 0 + 9 Reorder the terms: -9 + 9 + 2X + X2 = 0 + 9 Combine like terms: -9 + 9 = 0 0 + 2X + X2 = 0 + 9 2X + X2 = 0 + 9 Combine like terms: 0 + 9 = 9 2X + X2 = 9 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 = 9 + 1 Reorder the terms: 1 + 2X + X2 = 9 + 1 Combine like terms: 9 + 1 = 10 1 + 2X + X2 = 10 Factor a perfect square on the left side: (X + 1)(X + 1) = 10 Calculate the square root of the right side: 3.16227766 Break this problem into two subproblems by setting (X + 1) equal to 3.16227766 and -3.16227766.Subproblem 1
X + 1 = 3.16227766 Simplifying X + 1 = 3.16227766 Reorder the terms: 1 + X = 3.16227766 Solving 1 + X = 3.16227766 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 = 3.16227766 + -1 Combine like terms: 1 + -1 = 0 0 + X = 3.16227766 + -1 X = 3.16227766 + -1 Combine like terms: 3.16227766 + -1 = 2.16227766 X = 2.16227766 Simplifying X = 2.16227766Subproblem 2
X + 1 = -3.16227766 Simplifying X + 1 = -3.16227766 Reorder the terms: 1 + X = -3.16227766 Solving 1 + X = -3.16227766 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 = -3.16227766 + -1 Combine like terms: 1 + -1 = 0 0 + X = -3.16227766 + -1 X = -3.16227766 + -1 Combine like terms: -3.16227766 + -1 = -4.16227766 X = -4.16227766 Simplifying X = -4.16227766Solution
The solution to the problem is based on the solutions from the subproblems. X = {2.16227766, -4.16227766}
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