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Simplifying x2 + -16x + -307 = 0 Reorder the terms: -307 + -16x + x2 = 0 Solving -307 + -16x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '307' to each side of the equation. -307 + -16x + 307 + x2 = 0 + 307 Reorder the terms: -307 + 307 + -16x + x2 = 0 + 307 Combine like terms: -307 + 307 = 0 0 + -16x + x2 = 0 + 307 -16x + x2 = 0 + 307 Combine like terms: 0 + 307 = 307 -16x + x2 = 307 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 = 307 + 64 Reorder the terms: 64 + -16x + x2 = 307 + 64 Combine like terms: 307 + 64 = 371 64 + -16x + x2 = 371 Factor a perfect square on the left side: (x + -8)(x + -8) = 371 Calculate the square root of the right side: 19.261360284 Break this problem into two subproblems by setting (x + -8) equal to 19.261360284 and -19.261360284.Subproblem 1
x + -8 = 19.261360284 Simplifying x + -8 = 19.261360284 Reorder the terms: -8 + x = 19.261360284 Solving -8 + x = 19.261360284 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 = 19.261360284 + 8 Combine like terms: -8 + 8 = 0 0 + x = 19.261360284 + 8 x = 19.261360284 + 8 Combine like terms: 19.261360284 + 8 = 27.261360284 x = 27.261360284 Simplifying x = 27.261360284Subproblem 2
x + -8 = -19.261360284 Simplifying x + -8 = -19.261360284 Reorder the terms: -8 + x = -19.261360284 Solving -8 + x = -19.261360284 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 = -19.261360284 + 8 Combine like terms: -8 + 8 = 0 0 + x = -19.261360284 + 8 x = -19.261360284 + 8 Combine like terms: -19.261360284 + 8 = -11.261360284 x = -11.261360284 Simplifying x = -11.261360284Solution
The solution to the problem is based on the solutions from the subproblems. x = {27.261360284, -11.261360284}
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