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Simplifying x2 + -27x + 40 = 0 Reorder the terms: 40 + -27x + x2 = 0 Solving 40 + -27x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-40' to each side of the equation. 40 + -27x + -40 + x2 = 0 + -40 Reorder the terms: 40 + -40 + -27x + x2 = 0 + -40 Combine like terms: 40 + -40 = 0 0 + -27x + x2 = 0 + -40 -27x + x2 = 0 + -40 Combine like terms: 0 + -40 = -40 -27x + x2 = -40 The x term is -27x. Take half its coefficient (-13.5). Square it (182.25) and add it to both sides. Add '182.25' to each side of the equation. -27x + 182.25 + x2 = -40 + 182.25 Reorder the terms: 182.25 + -27x + x2 = -40 + 182.25 Combine like terms: -40 + 182.25 = 142.25 182.25 + -27x + x2 = 142.25 Factor a perfect square on the left side: (x + -13.5)(x + -13.5) = 142.25 Calculate the square root of the right side: 11.926860442 Break this problem into two subproblems by setting (x + -13.5) equal to 11.926860442 and -11.926860442.Subproblem 1
x + -13.5 = 11.926860442 Simplifying x + -13.5 = 11.926860442 Reorder the terms: -13.5 + x = 11.926860442 Solving -13.5 + x = 11.926860442 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '13.5' to each side of the equation. -13.5 + 13.5 + x = 11.926860442 + 13.5 Combine like terms: -13.5 + 13.5 = 0.0 0.0 + x = 11.926860442 + 13.5 x = 11.926860442 + 13.5 Combine like terms: 11.926860442 + 13.5 = 25.426860442 x = 25.426860442 Simplifying x = 25.426860442Subproblem 2
x + -13.5 = -11.926860442 Simplifying x + -13.5 = -11.926860442 Reorder the terms: -13.5 + x = -11.926860442 Solving -13.5 + x = -11.926860442 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '13.5' to each side of the equation. -13.5 + 13.5 + x = -11.926860442 + 13.5 Combine like terms: -13.5 + 13.5 = 0.0 0.0 + x = -11.926860442 + 13.5 x = -11.926860442 + 13.5 Combine like terms: -11.926860442 + 13.5 = 1.573139558 x = 1.573139558 Simplifying x = 1.573139558Solution
The solution to the problem is based on the solutions from the subproblems. x = {25.426860442, 1.573139558}
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