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Simplifying 1 + -1x2 + -11x + -6 = 0 Reorder the terms: 1 + -6 + -11x + -1x2 = 0 Combine like terms: 1 + -6 = -5 -5 + -11x + -1x2 = 0 Solving -5 + -11x + -1x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '-1'. -1(5 + 11x + x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(5 + 11x + x2)' equal to zero and attempt to solve: Simplifying 5 + 11x + x2 = 0 Solving 5 + 11x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-5' to each side of the equation. 5 + 11x + -5 + x2 = 0 + -5 Reorder the terms: 5 + -5 + 11x + x2 = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 11x + x2 = 0 + -5 11x + x2 = 0 + -5 Combine like terms: 0 + -5 = -5 11x + x2 = -5 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 = -5 + 30.25 Reorder the terms: 30.25 + 11x + x2 = -5 + 30.25 Combine like terms: -5 + 30.25 = 25.25 30.25 + 11x + x2 = 25.25 Factor a perfect square on the left side: (x + 5.5)(x + 5.5) = 25.25 Calculate the square root of the right side: 5.024937811 Break this problem into two subproblems by setting (x + 5.5) equal to 5.024937811 and -5.024937811.Subproblem 1
x + 5.5 = 5.024937811 Simplifying x + 5.5 = 5.024937811 Reorder the terms: 5.5 + x = 5.024937811 Solving 5.5 + x = 5.024937811 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 = 5.024937811 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + x = 5.024937811 + -5.5 x = 5.024937811 + -5.5 Combine like terms: 5.024937811 + -5.5 = -0.475062189 x = -0.475062189 Simplifying x = -0.475062189Subproblem 2
x + 5.5 = -5.024937811 Simplifying x + 5.5 = -5.024937811 Reorder the terms: 5.5 + x = -5.024937811 Solving 5.5 + x = -5.024937811 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 = -5.024937811 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + x = -5.024937811 + -5.5 x = -5.024937811 + -5.5 Combine like terms: -5.024937811 + -5.5 = -10.524937811 x = -10.524937811 Simplifying x = -10.524937811Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.475062189, -10.524937811}Solution
x = {-0.475062189, -10.524937811}
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