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Simplifying x2 + 16x + -660 = 0 Reorder the terms: -660 + 16x + x2 = 0 Solving -660 + 16x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '660' to each side of the equation. -660 + 16x + 660 + x2 = 0 + 660 Reorder the terms: -660 + 660 + 16x + x2 = 0 + 660 Combine like terms: -660 + 660 = 0 0 + 16x + x2 = 0 + 660 16x + x2 = 0 + 660 Combine like terms: 0 + 660 = 660 16x + x2 = 660 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 = 660 + 64 Reorder the terms: 64 + 16x + x2 = 660 + 64 Combine like terms: 660 + 64 = 724 64 + 16x + x2 = 724 Factor a perfect square on the left side: (x + 8)(x + 8) = 724 Calculate the square root of the right side: 26.907248094 Break this problem into two subproblems by setting (x + 8) equal to 26.907248094 and -26.907248094.Subproblem 1
x + 8 = 26.907248094 Simplifying x + 8 = 26.907248094 Reorder the terms: 8 + x = 26.907248094 Solving 8 + x = 26.907248094 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 = 26.907248094 + -8 Combine like terms: 8 + -8 = 0 0 + x = 26.907248094 + -8 x = 26.907248094 + -8 Combine like terms: 26.907248094 + -8 = 18.907248094 x = 18.907248094 Simplifying x = 18.907248094Subproblem 2
x + 8 = -26.907248094 Simplifying x + 8 = -26.907248094 Reorder the terms: 8 + x = -26.907248094 Solving 8 + x = -26.907248094 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 = -26.907248094 + -8 Combine like terms: 8 + -8 = 0 0 + x = -26.907248094 + -8 x = -26.907248094 + -8 Combine like terms: -26.907248094 + -8 = -34.907248094 x = -34.907248094 Simplifying x = -34.907248094Solution
The solution to the problem is based on the solutions from the subproblems. x = {18.907248094, -34.907248094}
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