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Simplifying 11x2 + -13x + -4 = 0 Reorder the terms: -4 + -13x + 11x2 = 0 Solving -4 + -13x + 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'. -0.3636363636 + -1.181818182x + x2 = 0 Move the constant term to the right: Add '0.3636363636' to each side of the equation. -0.3636363636 + -1.181818182x + 0.3636363636 + x2 = 0 + 0.3636363636 Reorder the terms: -0.3636363636 + 0.3636363636 + -1.181818182x + x2 = 0 + 0.3636363636 Combine like terms: -0.3636363636 + 0.3636363636 = 0.0000000000 0.0000000000 + -1.181818182x + x2 = 0 + 0.3636363636 -1.181818182x + x2 = 0 + 0.3636363636 Combine like terms: 0 + 0.3636363636 = 0.3636363636 -1.181818182x + x2 = 0.3636363636 The x term is -1.181818182x. Take half its coefficient (-0.590909091). Square it (0.3491735538) and add it to both sides. Add '0.3491735538' to each side of the equation. -1.181818182x + 0.3491735538 + x2 = 0.3636363636 + 0.3491735538 Reorder the terms: 0.3491735538 + -1.181818182x + x2 = 0.3636363636 + 0.3491735538 Combine like terms: 0.3636363636 + 0.3491735538 = 0.7128099174 0.3491735538 + -1.181818182x + x2 = 0.7128099174 Factor a perfect square on the left side: (x + -0.590909091)(x + -0.590909091) = 0.7128099174 Calculate the square root of the right side: 0.84428071 Break this problem into two subproblems by setting (x + -0.590909091) equal to 0.84428071 and -0.84428071.Subproblem 1
x + -0.590909091 = 0.84428071 Simplifying x + -0.590909091 = 0.84428071 Reorder the terms: -0.590909091 + x = 0.84428071 Solving -0.590909091 + x = 0.84428071 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.590909091' to each side of the equation. -0.590909091 + 0.590909091 + x = 0.84428071 + 0.590909091 Combine like terms: -0.590909091 + 0.590909091 = 0.000000000 0.000000000 + x = 0.84428071 + 0.590909091 x = 0.84428071 + 0.590909091 Combine like terms: 0.84428071 + 0.590909091 = 1.435189801 x = 1.435189801 Simplifying x = 1.435189801Subproblem 2
x + -0.590909091 = -0.84428071 Simplifying x + -0.590909091 = -0.84428071 Reorder the terms: -0.590909091 + x = -0.84428071 Solving -0.590909091 + x = -0.84428071 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.590909091' to each side of the equation. -0.590909091 + 0.590909091 + x = -0.84428071 + 0.590909091 Combine like terms: -0.590909091 + 0.590909091 = 0.000000000 0.000000000 + x = -0.84428071 + 0.590909091 x = -0.84428071 + 0.590909091 Combine like terms: -0.84428071 + 0.590909091 = -0.253371619 x = -0.253371619 Simplifying x = -0.253371619Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.435189801, -0.253371619}
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