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Simplifying x2 + 11x + -213 = 0 Reorder the terms: -213 + 11x + x2 = 0 Solving -213 + 11x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '213' to each side of the equation. -213 + 11x + 213 + x2 = 0 + 213 Reorder the terms: -213 + 213 + 11x + x2 = 0 + 213 Combine like terms: -213 + 213 = 0 0 + 11x + x2 = 0 + 213 11x + x2 = 0 + 213 Combine like terms: 0 + 213 = 213 11x + x2 = 213 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 = 213 + 30.25 Reorder the terms: 30.25 + 11x + x2 = 213 + 30.25 Combine like terms: 213 + 30.25 = 243.25 30.25 + 11x + x2 = 243.25 Factor a perfect square on the left side: (x + 5.5)(x + 5.5) = 243.25 Calculate the square root of the right side: 15.59647396 Break this problem into two subproblems by setting (x + 5.5) equal to 15.59647396 and -15.59647396.Subproblem 1
x + 5.5 = 15.59647396 Simplifying x + 5.5 = 15.59647396 Reorder the terms: 5.5 + x = 15.59647396 Solving 5.5 + x = 15.59647396 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 = 15.59647396 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + x = 15.59647396 + -5.5 x = 15.59647396 + -5.5 Combine like terms: 15.59647396 + -5.5 = 10.09647396 x = 10.09647396 Simplifying x = 10.09647396Subproblem 2
x + 5.5 = -15.59647396 Simplifying x + 5.5 = -15.59647396 Reorder the terms: 5.5 + x = -15.59647396 Solving 5.5 + x = -15.59647396 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 = -15.59647396 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + x = -15.59647396 + -5.5 x = -15.59647396 + -5.5 Combine like terms: -15.59647396 + -5.5 = -21.09647396 x = -21.09647396 Simplifying x = -21.09647396Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.09647396, -21.09647396}
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