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Simplifying x2 + 11x + 24.6 = 0 Reorder the terms: 24.6 + 11x + x2 = 0 Solving 24.6 + 11x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-24.6' to each side of the equation. 24.6 + 11x + -24.6 + x2 = 0 + -24.6 Reorder the terms: 24.6 + -24.6 + 11x + x2 = 0 + -24.6 Combine like terms: 24.6 + -24.6 = 0.0 0.0 + 11x + x2 = 0 + -24.6 11x + x2 = 0 + -24.6 Combine like terms: 0 + -24.6 = -24.6 11x + x2 = -24.6 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 = -24.6 + 30.25 Reorder the terms: 30.25 + 11x + x2 = -24.6 + 30.25 Combine like terms: -24.6 + 30.25 = 5.65 30.25 + 11x + x2 = 5.65 Factor a perfect square on the left side: (x + 5.5)(x + 5.5) = 5.65 Calculate the square root of the right side: 2.376972865 Break this problem into two subproblems by setting (x + 5.5) equal to 2.376972865 and -2.376972865.Subproblem 1
x + 5.5 = 2.376972865 Simplifying x + 5.5 = 2.376972865 Reorder the terms: 5.5 + x = 2.376972865 Solving 5.5 + x = 2.376972865 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 = 2.376972865 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + x = 2.376972865 + -5.5 x = 2.376972865 + -5.5 Combine like terms: 2.376972865 + -5.5 = -3.123027135 x = -3.123027135 Simplifying x = -3.123027135Subproblem 2
x + 5.5 = -2.376972865 Simplifying x + 5.5 = -2.376972865 Reorder the terms: 5.5 + x = -2.376972865 Solving 5.5 + x = -2.376972865 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 = -2.376972865 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + x = -2.376972865 + -5.5 x = -2.376972865 + -5.5 Combine like terms: -2.376972865 + -5.5 = -7.876972865 x = -7.876972865 Simplifying x = -7.876972865Solution
The solution to the problem is based on the solutions from the subproblems. x = {-3.123027135, -7.876972865}
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