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Simplifying X * X + 1X + 2 = 3360 Multiply X * X X2 + 1X + 2 = 3360 Reorder the terms: 2 + 1X + X2 = 3360 Solving 2 + 1X + X2 = 3360 Solving for variable 'X'. Reorder the terms: 2 + -3360 + 1X + X2 = 3360 + -3360 Combine like terms: 2 + -3360 = -3358 -3358 + 1X + X2 = 3360 + -3360 Combine like terms: 3360 + -3360 = 0 -3358 + 1X + X2 = 0 Begin completing the square. Move the constant term to the right: Add '3358' to each side of the equation. -3358 + 1X + 3358 + X2 = 0 + 3358 Reorder the terms: -3358 + 3358 + 1X + X2 = 0 + 3358 Combine like terms: -3358 + 3358 = 0 0 + 1X + X2 = 0 + 3358 1X + X2 = 0 + 3358 Combine like terms: 0 + 3358 = 3358 1X + X2 = 3358 The X term is 1X. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. X + 0.25 + X2 = 3358 + 0.25 Reorder the terms: 0.25 + X + X2 = 3358 + 0.25 Combine like terms: 3358 + 0.25 = 3358.25 0.25 + X + X2 = 3358.25 Factor a perfect square on the left side: (X + 0.5)(X + 0.5) = 3358.25 Calculate the square root of the right side: 57.950409835 Break this problem into two subproblems by setting (X + 0.5) equal to 57.950409835 and -57.950409835.Subproblem 1
X + 0.5 = 57.950409835 Simplifying X + 0.5 = 57.950409835 Reorder the terms: 0.5 + X = 57.950409835 Solving 0.5 + X = 57.950409835 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + X = 57.950409835 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + X = 57.950409835 + -0.5 X = 57.950409835 + -0.5 Combine like terms: 57.950409835 + -0.5 = 57.450409835 X = 57.450409835 Simplifying X = 57.450409835Subproblem 2
X + 0.5 = -57.950409835 Simplifying X + 0.5 = -57.950409835 Reorder the terms: 0.5 + X = -57.950409835 Solving 0.5 + X = -57.950409835 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + X = -57.950409835 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + X = -57.950409835 + -0.5 X = -57.950409835 + -0.5 Combine like terms: -57.950409835 + -0.5 = -58.450409835 X = -58.450409835 Simplifying X = -58.450409835Solution
The solution to the problem is based on the solutions from the subproblems. X = {57.450409835, -58.450409835}
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