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Simplifying x2 + -16x = -44 Reorder the terms: -16x + x2 = -44 Solving -16x + x2 = -44 Solving for variable 'x'. Reorder the terms: 44 + -16x + x2 = -44 + 44 Combine like terms: -44 + 44 = 0 44 + -16x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-44' to each side of the equation. 44 + -16x + -44 + x2 = 0 + -44 Reorder the terms: 44 + -44 + -16x + x2 = 0 + -44 Combine like terms: 44 + -44 = 0 0 + -16x + x2 = 0 + -44 -16x + x2 = 0 + -44 Combine like terms: 0 + -44 = -44 -16x + x2 = -44 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 = -44 + 64 Reorder the terms: 64 + -16x + x2 = -44 + 64 Combine like terms: -44 + 64 = 20 64 + -16x + x2 = 20 Factor a perfect square on the left side: (x + -8)(x + -8) = 20 Calculate the square root of the right side: 4.472135955 Break this problem into two subproblems by setting (x + -8) equal to 4.472135955 and -4.472135955.Subproblem 1
x + -8 = 4.472135955 Simplifying x + -8 = 4.472135955 Reorder the terms: -8 + x = 4.472135955 Solving -8 + x = 4.472135955 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 = 4.472135955 + 8 Combine like terms: -8 + 8 = 0 0 + x = 4.472135955 + 8 x = 4.472135955 + 8 Combine like terms: 4.472135955 + 8 = 12.472135955 x = 12.472135955 Simplifying x = 12.472135955Subproblem 2
x + -8 = -4.472135955 Simplifying x + -8 = -4.472135955 Reorder the terms: -8 + x = -4.472135955 Solving -8 + x = -4.472135955 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 = -4.472135955 + 8 Combine like terms: -8 + 8 = 0 0 + x = -4.472135955 + 8 x = -4.472135955 + 8 Combine like terms: -4.472135955 + 8 = 3.527864045 x = 3.527864045 Simplifying x = 3.527864045Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.472135955, 3.527864045}
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