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Simplifying x2 + 11x + -5 = 2 Reorder the terms: -5 + 11x + x2 = 2 Solving -5 + 11x + x2 = 2 Solving for variable 'x'. Reorder the terms: -5 + -2 + 11x + x2 = 2 + -2 Combine like terms: -5 + -2 = -7 -7 + 11x + x2 = 2 + -2 Combine like terms: 2 + -2 = 0 -7 + 11x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '7' to each side of the equation. -7 + 11x + 7 + x2 = 0 + 7 Reorder the terms: -7 + 7 + 11x + x2 = 0 + 7 Combine like terms: -7 + 7 = 0 0 + 11x + x2 = 0 + 7 11x + x2 = 0 + 7 Combine like terms: 0 + 7 = 7 11x + x2 = 7 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 = 7 + 30.25 Reorder the terms: 30.25 + 11x + x2 = 7 + 30.25 Combine like terms: 7 + 30.25 = 37.25 30.25 + 11x + x2 = 37.25 Factor a perfect square on the left side: (x + 5.5)(x + 5.5) = 37.25 Calculate the square root of the right side: 6.103277808 Break this problem into two subproblems by setting (x + 5.5) equal to 6.103277808 and -6.103277808.Subproblem 1
x + 5.5 = 6.103277808 Simplifying x + 5.5 = 6.103277808 Reorder the terms: 5.5 + x = 6.103277808 Solving 5.5 + x = 6.103277808 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 = 6.103277808 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + x = 6.103277808 + -5.5 x = 6.103277808 + -5.5 Combine like terms: 6.103277808 + -5.5 = 0.603277808 x = 0.603277808 Simplifying x = 0.603277808Subproblem 2
x + 5.5 = -6.103277808 Simplifying x + 5.5 = -6.103277808 Reorder the terms: 5.5 + x = -6.103277808 Solving 5.5 + x = -6.103277808 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 = -6.103277808 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + x = -6.103277808 + -5.5 x = -6.103277808 + -5.5 Combine like terms: -6.103277808 + -5.5 = -11.603277808 x = -11.603277808 Simplifying x = -11.603277808Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.603277808, -11.603277808}
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