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Simplifying X2 + -11X = 24 Reorder the terms: -11X + X2 = 24 Solving -11X + X2 = 24 Solving for variable 'X'. Reorder the terms: -24 + -11X + X2 = 24 + -24 Combine like terms: 24 + -24 = 0 -24 + -11X + X2 = 0 Begin completing the square. Move the constant term to the right: Add '24' to each side of the equation. -24 + -11X + 24 + X2 = 0 + 24 Reorder the terms: -24 + 24 + -11X + X2 = 0 + 24 Combine like terms: -24 + 24 = 0 0 + -11X + X2 = 0 + 24 -11X + X2 = 0 + 24 Combine like terms: 0 + 24 = 24 -11X + X2 = 24 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 = 24 + 30.25 Reorder the terms: 30.25 + -11X + X2 = 24 + 30.25 Combine like terms: 24 + 30.25 = 54.25 30.25 + -11X + X2 = 54.25 Factor a perfect square on the left side: (X + -5.5)(X + -5.5) = 54.25 Calculate the square root of the right side: 7.365459931 Break this problem into two subproblems by setting (X + -5.5) equal to 7.365459931 and -7.365459931.Subproblem 1
X + -5.5 = 7.365459931 Simplifying X + -5.5 = 7.365459931 Reorder the terms: -5.5 + X = 7.365459931 Solving -5.5 + X = 7.365459931 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 = 7.365459931 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + X = 7.365459931 + 5.5 X = 7.365459931 + 5.5 Combine like terms: 7.365459931 + 5.5 = 12.865459931 X = 12.865459931 Simplifying X = 12.865459931Subproblem 2
X + -5.5 = -7.365459931 Simplifying X + -5.5 = -7.365459931 Reorder the terms: -5.5 + X = -7.365459931 Solving -5.5 + X = -7.365459931 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 = -7.365459931 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + X = -7.365459931 + 5.5 X = -7.365459931 + 5.5 Combine like terms: -7.365459931 + 5.5 = -1.865459931 X = -1.865459931 Simplifying X = -1.865459931Solution
The solution to the problem is based on the solutions from the subproblems. X = {12.865459931, -1.865459931}
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