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Simplifying 5x2 + -18x + -11 = 0 Reorder the terms: -11 + -18x + 5x2 = 0 Solving -11 + -18x + 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'. -2.2 + -3.6x + x2 = 0 Move the constant term to the right: Add '2.2' to each side of the equation. -2.2 + -3.6x + 2.2 + x2 = 0 + 2.2 Reorder the terms: -2.2 + 2.2 + -3.6x + x2 = 0 + 2.2 Combine like terms: -2.2 + 2.2 = 0.0 0.0 + -3.6x + x2 = 0 + 2.2 -3.6x + x2 = 0 + 2.2 Combine like terms: 0 + 2.2 = 2.2 -3.6x + x2 = 2.2 The x term is -3.6x. Take half its coefficient (-1.8). Square it (3.24) and add it to both sides. Add '3.24' to each side of the equation. -3.6x + 3.24 + x2 = 2.2 + 3.24 Reorder the terms: 3.24 + -3.6x + x2 = 2.2 + 3.24 Combine like terms: 2.2 + 3.24 = 5.44 3.24 + -3.6x + x2 = 5.44 Factor a perfect square on the left side: (x + -1.8)(x + -1.8) = 5.44 Calculate the square root of the right side: 2.332380758 Break this problem into two subproblems by setting (x + -1.8) equal to 2.332380758 and -2.332380758.Subproblem 1
x + -1.8 = 2.332380758 Simplifying x + -1.8 = 2.332380758 Reorder the terms: -1.8 + x = 2.332380758 Solving -1.8 + x = 2.332380758 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.8' to each side of the equation. -1.8 + 1.8 + x = 2.332380758 + 1.8 Combine like terms: -1.8 + 1.8 = 0.0 0.0 + x = 2.332380758 + 1.8 x = 2.332380758 + 1.8 Combine like terms: 2.332380758 + 1.8 = 4.132380758 x = 4.132380758 Simplifying x = 4.132380758Subproblem 2
x + -1.8 = -2.332380758 Simplifying x + -1.8 = -2.332380758 Reorder the terms: -1.8 + x = -2.332380758 Solving -1.8 + x = -2.332380758 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.8' to each side of the equation. -1.8 + 1.8 + x = -2.332380758 + 1.8 Combine like terms: -1.8 + 1.8 = 0.0 0.0 + x = -2.332380758 + 1.8 x = -2.332380758 + 1.8 Combine like terms: -2.332380758 + 1.8 = -0.532380758 x = -0.532380758 Simplifying x = -0.532380758Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.132380758, -0.532380758}
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