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Simplifying x2 + 11x + 15 = 0 Reorder the terms: 15 + 11x + x2 = 0 Solving 15 + 11x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-15' to each side of the equation. 15 + 11x + -15 + x2 = 0 + -15 Reorder the terms: 15 + -15 + 11x + x2 = 0 + -15 Combine like terms: 15 + -15 = 0 0 + 11x + x2 = 0 + -15 11x + x2 = 0 + -15 Combine like terms: 0 + -15 = -15 11x + x2 = -15 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 = -15 + 30.25 Reorder the terms: 30.25 + 11x + x2 = -15 + 30.25 Combine like terms: -15 + 30.25 = 15.25 30.25 + 11x + x2 = 15.25 Factor a perfect square on the left side: (x + 5.5)(x + 5.5) = 15.25 Calculate the square root of the right side: 3.905124838 Break this problem into two subproblems by setting (x + 5.5) equal to 3.905124838 and -3.905124838.Subproblem 1
x + 5.5 = 3.905124838 Simplifying x + 5.5 = 3.905124838 Reorder the terms: 5.5 + x = 3.905124838 Solving 5.5 + x = 3.905124838 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 = 3.905124838 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + x = 3.905124838 + -5.5 x = 3.905124838 + -5.5 Combine like terms: 3.905124838 + -5.5 = -1.594875162 x = -1.594875162 Simplifying x = -1.594875162Subproblem 2
x + 5.5 = -3.905124838 Simplifying x + 5.5 = -3.905124838 Reorder the terms: 5.5 + x = -3.905124838 Solving 5.5 + x = -3.905124838 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 = -3.905124838 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + x = -3.905124838 + -5.5 x = -3.905124838 + -5.5 Combine like terms: -3.905124838 + -5.5 = -9.405124838 x = -9.405124838 Simplifying x = -9.405124838Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.594875162, -9.405124838}
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