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Simplifying x2 + -9x + -27 = 4 Reorder the terms: -27 + -9x + x2 = 4 Solving -27 + -9x + x2 = 4 Solving for variable 'x'. Reorder the terms: -27 + -4 + -9x + x2 = 4 + -4 Combine like terms: -27 + -4 = -31 -31 + -9x + x2 = 4 + -4 Combine like terms: 4 + -4 = 0 -31 + -9x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '31' to each side of the equation. -31 + -9x + 31 + x2 = 0 + 31 Reorder the terms: -31 + 31 + -9x + x2 = 0 + 31 Combine like terms: -31 + 31 = 0 0 + -9x + x2 = 0 + 31 -9x + x2 = 0 + 31 Combine like terms: 0 + 31 = 31 -9x + x2 = 31 The x term is -9x. Take half its coefficient (-4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. -9x + 20.25 + x2 = 31 + 20.25 Reorder the terms: 20.25 + -9x + x2 = 31 + 20.25 Combine like terms: 31 + 20.25 = 51.25 20.25 + -9x + x2 = 51.25 Factor a perfect square on the left side: (x + -4.5)(x + -4.5) = 51.25 Calculate the square root of the right side: 7.158910532 Break this problem into two subproblems by setting (x + -4.5) equal to 7.158910532 and -7.158910532.Subproblem 1
x + -4.5 = 7.158910532 Simplifying x + -4.5 = 7.158910532 Reorder the terms: -4.5 + x = 7.158910532 Solving -4.5 + x = 7.158910532 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + x = 7.158910532 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = 7.158910532 + 4.5 x = 7.158910532 + 4.5 Combine like terms: 7.158910532 + 4.5 = 11.658910532 x = 11.658910532 Simplifying x = 11.658910532Subproblem 2
x + -4.5 = -7.158910532 Simplifying x + -4.5 = -7.158910532 Reorder the terms: -4.5 + x = -7.158910532 Solving -4.5 + x = -7.158910532 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + x = -7.158910532 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = -7.158910532 + 4.5 x = -7.158910532 + 4.5 Combine like terms: -7.158910532 + 4.5 = -2.658910532 x = -2.658910532 Simplifying x = -2.658910532Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.658910532, -2.658910532}
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