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Simplifying 0 = x2 + 5x + -11 Reorder the terms: 0 = -11 + 5x + x2 Solving 0 = -11 + 5x + x2 Solving for variable 'x'. Combine like terms: 0 + 11 = 11 11 + -5x + -1x2 = -11 + 5x + x2 + 11 + -5x + -1x2 Reorder the terms: 11 + -5x + -1x2 = -11 + 11 + 5x + -5x + x2 + -1x2 Combine like terms: -11 + 11 = 0 11 + -5x + -1x2 = 0 + 5x + -5x + x2 + -1x2 11 + -5x + -1x2 = 5x + -5x + x2 + -1x2 Combine like terms: 5x + -5x = 0 11 + -5x + -1x2 = 0 + x2 + -1x2 11 + -5x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 11 + -5x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -11 + 5x + x2 = 0 Move the constant term to the right: Add '11' to each side of the equation. -11 + 5x + 11 + x2 = 0 + 11 Reorder the terms: -11 + 11 + 5x + x2 = 0 + 11 Combine like terms: -11 + 11 = 0 0 + 5x + x2 = 0 + 11 5x + x2 = 0 + 11 Combine like terms: 0 + 11 = 11 5x + x2 = 11 The x term is 5x. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5x + 6.25 + x2 = 11 + 6.25 Reorder the terms: 6.25 + 5x + x2 = 11 + 6.25 Combine like terms: 11 + 6.25 = 17.25 6.25 + 5x + x2 = 17.25 Factor a perfect square on the left side: (x + 2.5)(x + 2.5) = 17.25 Calculate the square root of the right side: 4.153311931 Break this problem into two subproblems by setting (x + 2.5) equal to 4.153311931 and -4.153311931.Subproblem 1
x + 2.5 = 4.153311931 Simplifying x + 2.5 = 4.153311931 Reorder the terms: 2.5 + x = 4.153311931 Solving 2.5 + x = 4.153311931 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = 4.153311931 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 4.153311931 + -2.5 x = 4.153311931 + -2.5 Combine like terms: 4.153311931 + -2.5 = 1.653311931 x = 1.653311931 Simplifying x = 1.653311931Subproblem 2
x + 2.5 = -4.153311931 Simplifying x + 2.5 = -4.153311931 Reorder the terms: 2.5 + x = -4.153311931 Solving 2.5 + x = -4.153311931 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = -4.153311931 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -4.153311931 + -2.5 x = -4.153311931 + -2.5 Combine like terms: -4.153311931 + -2.5 = -6.653311931 x = -6.653311931 Simplifying x = -6.653311931Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.653311931, -6.653311931}
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