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Simplifying x2 + -5.4x + -6 = 0 Reorder the terms: -6 + -5.4x + x2 = 0 Solving -6 + -5.4x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '6' to each side of the equation. -6 + -5.4x + 6 + x2 = 0 + 6 Reorder the terms: -6 + 6 + -5.4x + x2 = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -5.4x + x2 = 0 + 6 -5.4x + x2 = 0 + 6 Combine like terms: 0 + 6 = 6 -5.4x + x2 = 6 The x term is -5.4x. Take half its coefficient (-2.7). Square it (7.29) and add it to both sides. Add '7.29' to each side of the equation. -5.4x + 7.29 + x2 = 6 + 7.29 Reorder the terms: 7.29 + -5.4x + x2 = 6 + 7.29 Combine like terms: 6 + 7.29 = 13.29 7.29 + -5.4x + x2 = 13.29 Factor a perfect square on the left side: (x + -2.7)(x + -2.7) = 13.29 Calculate the square root of the right side: 3.645545227 Break this problem into two subproblems by setting (x + -2.7) equal to 3.645545227 and -3.645545227.Subproblem 1
x + -2.7 = 3.645545227 Simplifying x + -2.7 = 3.645545227 Reorder the terms: -2.7 + x = 3.645545227 Solving -2.7 + x = 3.645545227 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.7' to each side of the equation. -2.7 + 2.7 + x = 3.645545227 + 2.7 Combine like terms: -2.7 + 2.7 = 0.0 0.0 + x = 3.645545227 + 2.7 x = 3.645545227 + 2.7 Combine like terms: 3.645545227 + 2.7 = 6.345545227 x = 6.345545227 Simplifying x = 6.345545227Subproblem 2
x + -2.7 = -3.645545227 Simplifying x + -2.7 = -3.645545227 Reorder the terms: -2.7 + x = -3.645545227 Solving -2.7 + x = -3.645545227 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.7' to each side of the equation. -2.7 + 2.7 + x = -3.645545227 + 2.7 Combine like terms: -2.7 + 2.7 = 0.0 0.0 + x = -3.645545227 + 2.7 x = -3.645545227 + 2.7 Combine like terms: -3.645545227 + 2.7 = -0.945545227 x = -0.945545227 Simplifying x = -0.945545227Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.345545227, -0.945545227}
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