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Simplifying x2 + -16x + -27 = 0 Reorder the terms: -27 + -16x + x2 = 0 Solving -27 + -16x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '27' to each side of the equation. -27 + -16x + 27 + x2 = 0 + 27 Reorder the terms: -27 + 27 + -16x + x2 = 0 + 27 Combine like terms: -27 + 27 = 0 0 + -16x + x2 = 0 + 27 -16x + x2 = 0 + 27 Combine like terms: 0 + 27 = 27 -16x + x2 = 27 The x term is -16x. Take half its coefficient (-8). Square it (64) and add it to both sides. Add '64' to each side of the equation. -16x + 64 + x2 = 27 + 64 Reorder the terms: 64 + -16x + x2 = 27 + 64 Combine like terms: 27 + 64 = 91 64 + -16x + x2 = 91 Factor a perfect square on the left side: (x + -8)(x + -8) = 91 Calculate the square root of the right side: 9.539392014 Break this problem into two subproblems by setting (x + -8) equal to 9.539392014 and -9.539392014.Subproblem 1
x + -8 = 9.539392014 Simplifying x + -8 = 9.539392014 Reorder the terms: -8 + x = 9.539392014 Solving -8 + x = 9.539392014 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + x = 9.539392014 + 8 Combine like terms: -8 + 8 = 0 0 + x = 9.539392014 + 8 x = 9.539392014 + 8 Combine like terms: 9.539392014 + 8 = 17.539392014 x = 17.539392014 Simplifying x = 17.539392014Subproblem 2
x + -8 = -9.539392014 Simplifying x + -8 = -9.539392014 Reorder the terms: -8 + x = -9.539392014 Solving -8 + x = -9.539392014 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + x = -9.539392014 + 8 Combine like terms: -8 + 8 = 0 0 + x = -9.539392014 + 8 x = -9.539392014 + 8 Combine like terms: -9.539392014 + 8 = -1.539392014 x = -1.539392014 Simplifying x = -1.539392014Solution
The solution to the problem is based on the solutions from the subproblems. x = {17.539392014, -1.539392014}
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