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Simplifying x2 + -16x + -71 = 0 Reorder the terms: -71 + -16x + x2 = 0 Solving -71 + -16x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '71' to each side of the equation. -71 + -16x + 71 + x2 = 0 + 71 Reorder the terms: -71 + 71 + -16x + x2 = 0 + 71 Combine like terms: -71 + 71 = 0 0 + -16x + x2 = 0 + 71 -16x + x2 = 0 + 71 Combine like terms: 0 + 71 = 71 -16x + x2 = 71 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 = 71 + 64 Reorder the terms: 64 + -16x + x2 = 71 + 64 Combine like terms: 71 + 64 = 135 64 + -16x + x2 = 135 Factor a perfect square on the left side: (x + -8)(x + -8) = 135 Calculate the square root of the right side: 11.618950039 Break this problem into two subproblems by setting (x + -8) equal to 11.618950039 and -11.618950039.Subproblem 1
x + -8 = 11.618950039 Simplifying x + -8 = 11.618950039 Reorder the terms: -8 + x = 11.618950039 Solving -8 + x = 11.618950039 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 = 11.618950039 + 8 Combine like terms: -8 + 8 = 0 0 + x = 11.618950039 + 8 x = 11.618950039 + 8 Combine like terms: 11.618950039 + 8 = 19.618950039 x = 19.618950039 Simplifying x = 19.618950039Subproblem 2
x + -8 = -11.618950039 Simplifying x + -8 = -11.618950039 Reorder the terms: -8 + x = -11.618950039 Solving -8 + x = -11.618950039 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 = -11.618950039 + 8 Combine like terms: -8 + 8 = 0 0 + x = -11.618950039 + 8 x = -11.618950039 + 8 Combine like terms: -11.618950039 + 8 = -3.618950039 x = -3.618950039 Simplifying x = -3.618950039Solution
The solution to the problem is based on the solutions from the subproblems. x = {19.618950039, -3.618950039}
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