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Simplifying x2 = 16x + 19 Reorder the terms: x2 = 19 + 16x Solving x2 = 19 + 16x Solving for variable 'x'. Reorder the terms: -19 + -16x + x2 = 19 + 16x + -19 + -16x Reorder the terms: -19 + -16x + x2 = 19 + -19 + 16x + -16x Combine like terms: 19 + -19 = 0 -19 + -16x + x2 = 0 + 16x + -16x -19 + -16x + x2 = 16x + -16x Combine like terms: 16x + -16x = 0 -19 + -16x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '19' to each side of the equation. -19 + -16x + 19 + x2 = 0 + 19 Reorder the terms: -19 + 19 + -16x + x2 = 0 + 19 Combine like terms: -19 + 19 = 0 0 + -16x + x2 = 0 + 19 -16x + x2 = 0 + 19 Combine like terms: 0 + 19 = 19 -16x + x2 = 19 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 = 19 + 64 Reorder the terms: 64 + -16x + x2 = 19 + 64 Combine like terms: 19 + 64 = 83 64 + -16x + x2 = 83 Factor a perfect square on the left side: (x + -8)(x + -8) = 83 Calculate the square root of the right side: 9.110433579 Break this problem into two subproblems by setting (x + -8) equal to 9.110433579 and -9.110433579.Subproblem 1
x + -8 = 9.110433579 Simplifying x + -8 = 9.110433579 Reorder the terms: -8 + x = 9.110433579 Solving -8 + x = 9.110433579 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 = 9.110433579 + 8 Combine like terms: -8 + 8 = 0 0 + x = 9.110433579 + 8 x = 9.110433579 + 8 Combine like terms: 9.110433579 + 8 = 17.110433579 x = 17.110433579 Simplifying x = 17.110433579Subproblem 2
x + -8 = -9.110433579 Simplifying x + -8 = -9.110433579 Reorder the terms: -8 + x = -9.110433579 Solving -8 + x = -9.110433579 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 = -9.110433579 + 8 Combine like terms: -8 + 8 = 0 0 + x = -9.110433579 + 8 x = -9.110433579 + 8 Combine like terms: -9.110433579 + 8 = -1.110433579 x = -1.110433579 Simplifying x = -1.110433579Solution
The solution to the problem is based on the solutions from the subproblems. x = {17.110433579, -1.110433579}
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