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Simplifying x2 + -16x + 56 = 0 Reorder the terms: 56 + -16x + x2 = 0 Solving 56 + -16x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-56' to each side of the equation. 56 + -16x + -56 + x2 = 0 + -56 Reorder the terms: 56 + -56 + -16x + x2 = 0 + -56 Combine like terms: 56 + -56 = 0 0 + -16x + x2 = 0 + -56 -16x + x2 = 0 + -56 Combine like terms: 0 + -56 = -56 -16x + x2 = -56 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 = -56 + 64 Reorder the terms: 64 + -16x + x2 = -56 + 64 Combine like terms: -56 + 64 = 8 64 + -16x + x2 = 8 Factor a perfect square on the left side: (x + -8)(x + -8) = 8 Calculate the square root of the right side: 2.828427125 Break this problem into two subproblems by setting (x + -8) equal to 2.828427125 and -2.828427125.Subproblem 1
x + -8 = 2.828427125 Simplifying x + -8 = 2.828427125 Reorder the terms: -8 + x = 2.828427125 Solving -8 + x = 2.828427125 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 = 2.828427125 + 8 Combine like terms: -8 + 8 = 0 0 + x = 2.828427125 + 8 x = 2.828427125 + 8 Combine like terms: 2.828427125 + 8 = 10.828427125 x = 10.828427125 Simplifying x = 10.828427125Subproblem 2
x + -8 = -2.828427125 Simplifying x + -8 = -2.828427125 Reorder the terms: -8 + x = -2.828427125 Solving -8 + x = -2.828427125 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 = -2.828427125 + 8 Combine like terms: -8 + 8 = 0 0 + x = -2.828427125 + 8 x = -2.828427125 + 8 Combine like terms: -2.828427125 + 8 = 5.171572875 x = 5.171572875 Simplifying x = 5.171572875Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.828427125, 5.171572875}
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