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Simplifying x2 + 16x + -280 = 0 Reorder the terms: -280 + 16x + x2 = 0 Solving -280 + 16x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '280' to each side of the equation. -280 + 16x + 280 + x2 = 0 + 280 Reorder the terms: -280 + 280 + 16x + x2 = 0 + 280 Combine like terms: -280 + 280 = 0 0 + 16x + x2 = 0 + 280 16x + x2 = 0 + 280 Combine like terms: 0 + 280 = 280 16x + x2 = 280 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 = 280 + 64 Reorder the terms: 64 + 16x + x2 = 280 + 64 Combine like terms: 280 + 64 = 344 64 + 16x + x2 = 344 Factor a perfect square on the left side: (x + 8)(x + 8) = 344 Calculate the square root of the right side: 18.547236991 Break this problem into two subproblems by setting (x + 8) equal to 18.547236991 and -18.547236991.Subproblem 1
x + 8 = 18.547236991 Simplifying x + 8 = 18.547236991 Reorder the terms: 8 + x = 18.547236991 Solving 8 + x = 18.547236991 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 = 18.547236991 + -8 Combine like terms: 8 + -8 = 0 0 + x = 18.547236991 + -8 x = 18.547236991 + -8 Combine like terms: 18.547236991 + -8 = 10.547236991 x = 10.547236991 Simplifying x = 10.547236991Subproblem 2
x + 8 = -18.547236991 Simplifying x + 8 = -18.547236991 Reorder the terms: 8 + x = -18.547236991 Solving 8 + x = -18.547236991 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 = -18.547236991 + -8 Combine like terms: 8 + -8 = 0 0 + x = -18.547236991 + -8 x = -18.547236991 + -8 Combine like terms: -18.547236991 + -8 = -26.547236991 x = -26.547236991 Simplifying x = -26.547236991Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.547236991, -26.547236991}
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