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Simplifying X2 + 11X + -450 = 0 Reorder the terms: -450 + 11X + X2 = 0 Solving -450 + 11X + X2 = 0 Solving for variable 'X'. Begin completing the square. Move the constant term to the right: Add '450' to each side of the equation. -450 + 11X + 450 + X2 = 0 + 450 Reorder the terms: -450 + 450 + 11X + X2 = 0 + 450 Combine like terms: -450 + 450 = 0 0 + 11X + X2 = 0 + 450 11X + X2 = 0 + 450 Combine like terms: 0 + 450 = 450 11X + X2 = 450 The X term is 11X. Take half its coefficient (5.5). Square it (30.25) and add it to both sides. Add '30.25' to each side of the equation. 11X + 30.25 + X2 = 450 + 30.25 Reorder the terms: 30.25 + 11X + X2 = 450 + 30.25 Combine like terms: 450 + 30.25 = 480.25 30.25 + 11X + X2 = 480.25 Factor a perfect square on the left side: (X + 5.5)(X + 5.5) = 480.25 Calculate the square root of the right side: 21.914607001 Break this problem into two subproblems by setting (X + 5.5) equal to 21.914607001 and -21.914607001.Subproblem 1
X + 5.5 = 21.914607001 Simplifying X + 5.5 = 21.914607001 Reorder the terms: 5.5 + X = 21.914607001 Solving 5.5 + X = 21.914607001 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-5.5' to each side of the equation. 5.5 + -5.5 + X = 21.914607001 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + X = 21.914607001 + -5.5 X = 21.914607001 + -5.5 Combine like terms: 21.914607001 + -5.5 = 16.414607001 X = 16.414607001 Simplifying X = 16.414607001Subproblem 2
X + 5.5 = -21.914607001 Simplifying X + 5.5 = -21.914607001 Reorder the terms: 5.5 + X = -21.914607001 Solving 5.5 + X = -21.914607001 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-5.5' to each side of the equation. 5.5 + -5.5 + X = -21.914607001 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + X = -21.914607001 + -5.5 X = -21.914607001 + -5.5 Combine like terms: -21.914607001 + -5.5 = -27.414607001 X = -27.414607001 Simplifying X = -27.414607001Solution
The solution to the problem is based on the solutions from the subproblems. X = {16.414607001, -27.414607001}
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