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Simplifying x2 + -16x + 64 = 23 Reorder the terms: 64 + -16x + x2 = 23 Solving 64 + -16x + x2 = 23 Solving for variable 'x'. Reorder the terms: 64 + -23 + -16x + x2 = 23 + -23 Combine like terms: 64 + -23 = 41 41 + -16x + x2 = 23 + -23 Combine like terms: 23 + -23 = 0 41 + -16x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-41' to each side of the equation. 41 + -16x + -41 + x2 = 0 + -41 Reorder the terms: 41 + -41 + -16x + x2 = 0 + -41 Combine like terms: 41 + -41 = 0 0 + -16x + x2 = 0 + -41 -16x + x2 = 0 + -41 Combine like terms: 0 + -41 = -41 -16x + x2 = -41 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 = -41 + 64 Reorder the terms: 64 + -16x + x2 = -41 + 64 Combine like terms: -41 + 64 = 23 64 + -16x + x2 = 23 Factor a perfect square on the left side: (x + -8)(x + -8) = 23 Calculate the square root of the right side: 4.795831523 Break this problem into two subproblems by setting (x + -8) equal to 4.795831523 and -4.795831523.Subproblem 1
x + -8 = 4.795831523 Simplifying x + -8 = 4.795831523 Reorder the terms: -8 + x = 4.795831523 Solving -8 + x = 4.795831523 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 = 4.795831523 + 8 Combine like terms: -8 + 8 = 0 0 + x = 4.795831523 + 8 x = 4.795831523 + 8 Combine like terms: 4.795831523 + 8 = 12.795831523 x = 12.795831523 Simplifying x = 12.795831523Subproblem 2
x + -8 = -4.795831523 Simplifying x + -8 = -4.795831523 Reorder the terms: -8 + x = -4.795831523 Solving -8 + x = -4.795831523 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 = -4.795831523 + 8 Combine like terms: -8 + 8 = 0 0 + x = -4.795831523 + 8 x = -4.795831523 + 8 Combine like terms: -4.795831523 + 8 = 3.204168477 x = 3.204168477 Simplifying x = 3.204168477Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.795831523, 3.204168477}
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