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Simplifying 11x2 + 14x + -13 = 0 Reorder the terms: -13 + 14x + 11x2 = 0 Solving -13 + 14x + 11x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 11 the coefficient of the squared term: Divide each side by '11'. -1.181818182 + 1.272727273x + x2 = 0 Move the constant term to the right: Add '1.181818182' to each side of the equation. -1.181818182 + 1.272727273x + 1.181818182 + x2 = 0 + 1.181818182 Reorder the terms: -1.181818182 + 1.181818182 + 1.272727273x + x2 = 0 + 1.181818182 Combine like terms: -1.181818182 + 1.181818182 = 0.000000000 0.000000000 + 1.272727273x + x2 = 0 + 1.181818182 1.272727273x + x2 = 0 + 1.181818182 Combine like terms: 0 + 1.181818182 = 1.181818182 1.272727273x + x2 = 1.181818182 The x term is 1.272727273x. Take half its coefficient (0.6363636365). Square it (0.4049586779) and add it to both sides. Add '0.4049586779' to each side of the equation. 1.272727273x + 0.4049586779 + x2 = 1.181818182 + 0.4049586779 Reorder the terms: 0.4049586779 + 1.272727273x + x2 = 1.181818182 + 0.4049586779 Combine like terms: 1.181818182 + 0.4049586779 = 1.5867768599 0.4049586779 + 1.272727273x + x2 = 1.5867768599 Factor a perfect square on the left side: (x + 0.6363636365)(x + 0.6363636365) = 1.5867768599 Calculate the square root of the right side: 1.259673315 Break this problem into two subproblems by setting (x + 0.6363636365) equal to 1.259673315 and -1.259673315.Subproblem 1
x + 0.6363636365 = 1.259673315 Simplifying x + 0.6363636365 = 1.259673315 Reorder the terms: 0.6363636365 + x = 1.259673315 Solving 0.6363636365 + x = 1.259673315 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.6363636365' to each side of the equation. 0.6363636365 + -0.6363636365 + x = 1.259673315 + -0.6363636365 Combine like terms: 0.6363636365 + -0.6363636365 = 0.0000000000 0.0000000000 + x = 1.259673315 + -0.6363636365 x = 1.259673315 + -0.6363636365 Combine like terms: 1.259673315 + -0.6363636365 = 0.6233096785 x = 0.6233096785 Simplifying x = 0.6233096785Subproblem 2
x + 0.6363636365 = -1.259673315 Simplifying x + 0.6363636365 = -1.259673315 Reorder the terms: 0.6363636365 + x = -1.259673315 Solving 0.6363636365 + x = -1.259673315 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.6363636365' to each side of the equation. 0.6363636365 + -0.6363636365 + x = -1.259673315 + -0.6363636365 Combine like terms: 0.6363636365 + -0.6363636365 = 0.0000000000 0.0000000000 + x = -1.259673315 + -0.6363636365 x = -1.259673315 + -0.6363636365 Combine like terms: -1.259673315 + -0.6363636365 = -1.8960369515 x = -1.8960369515 Simplifying x = -1.8960369515Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.6233096785, -1.8960369515}
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