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Simplifying 5x2 + -11x + -6 = 0 Reorder the terms: -6 + -11x + 5x2 = 0 Solving -6 + -11x + 5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -1.2 + -2.2x + x2 = 0 Move the constant term to the right: Add '1.2' to each side of the equation. -1.2 + -2.2x + 1.2 + x2 = 0 + 1.2 Reorder the terms: -1.2 + 1.2 + -2.2x + x2 = 0 + 1.2 Combine like terms: -1.2 + 1.2 = 0.0 0.0 + -2.2x + x2 = 0 + 1.2 -2.2x + x2 = 0 + 1.2 Combine like terms: 0 + 1.2 = 1.2 -2.2x + x2 = 1.2 The x term is -2.2x. Take half its coefficient (-1.1). Square it (1.21) and add it to both sides. Add '1.21' to each side of the equation. -2.2x + 1.21 + x2 = 1.2 + 1.21 Reorder the terms: 1.21 + -2.2x + x2 = 1.2 + 1.21 Combine like terms: 1.2 + 1.21 = 2.41 1.21 + -2.2x + x2 = 2.41 Factor a perfect square on the left side: (x + -1.1)(x + -1.1) = 2.41 Calculate the square root of the right side: 1.55241747 Break this problem into two subproblems by setting (x + -1.1) equal to 1.55241747 and -1.55241747.Subproblem 1
x + -1.1 = 1.55241747 Simplifying x + -1.1 = 1.55241747 Reorder the terms: -1.1 + x = 1.55241747 Solving -1.1 + x = 1.55241747 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.1' to each side of the equation. -1.1 + 1.1 + x = 1.55241747 + 1.1 Combine like terms: -1.1 + 1.1 = 0.0 0.0 + x = 1.55241747 + 1.1 x = 1.55241747 + 1.1 Combine like terms: 1.55241747 + 1.1 = 2.65241747 x = 2.65241747 Simplifying x = 2.65241747Subproblem 2
x + -1.1 = -1.55241747 Simplifying x + -1.1 = -1.55241747 Reorder the terms: -1.1 + x = -1.55241747 Solving -1.1 + x = -1.55241747 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.1' to each side of the equation. -1.1 + 1.1 + x = -1.55241747 + 1.1 Combine like terms: -1.1 + 1.1 = 0.0 0.0 + x = -1.55241747 + 1.1 x = -1.55241747 + 1.1 Combine like terms: -1.55241747 + 1.1 = -0.45241747 x = -0.45241747 Simplifying x = -0.45241747Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.65241747, -0.45241747}
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