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Simplifying x2 + -16x + 61 = 0 Reorder the terms: 61 + -16x + x2 = 0 Solving 61 + -16x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-61' to each side of the equation. 61 + -16x + -61 + x2 = 0 + -61 Reorder the terms: 61 + -61 + -16x + x2 = 0 + -61 Combine like terms: 61 + -61 = 0 0 + -16x + x2 = 0 + -61 -16x + x2 = 0 + -61 Combine like terms: 0 + -61 = -61 -16x + x2 = -61 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 = -61 + 64 Reorder the terms: 64 + -16x + x2 = -61 + 64 Combine like terms: -61 + 64 = 3 64 + -16x + x2 = 3 Factor a perfect square on the left side: (x + -8)(x + -8) = 3 Calculate the square root of the right side: 1.732050808 Break this problem into two subproblems by setting (x + -8) equal to 1.732050808 and -1.732050808.Subproblem 1
x + -8 = 1.732050808 Simplifying x + -8 = 1.732050808 Reorder the terms: -8 + x = 1.732050808 Solving -8 + x = 1.732050808 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 = 1.732050808 + 8 Combine like terms: -8 + 8 = 0 0 + x = 1.732050808 + 8 x = 1.732050808 + 8 Combine like terms: 1.732050808 + 8 = 9.732050808 x = 9.732050808 Simplifying x = 9.732050808Subproblem 2
x + -8 = -1.732050808 Simplifying x + -8 = -1.732050808 Reorder the terms: -8 + x = -1.732050808 Solving -8 + x = -1.732050808 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 = -1.732050808 + 8 Combine like terms: -8 + 8 = 0 0 + x = -1.732050808 + 8 x = -1.732050808 + 8 Combine like terms: -1.732050808 + 8 = 6.267949192 x = 6.267949192 Simplifying x = 6.267949192Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.732050808, 6.267949192}
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