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Simplifying x2 + -16x + 51 = 0 Reorder the terms: 51 + -16x + x2 = 0 Solving 51 + -16x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-51' to each side of the equation. 51 + -16x + -51 + x2 = 0 + -51 Reorder the terms: 51 + -51 + -16x + x2 = 0 + -51 Combine like terms: 51 + -51 = 0 0 + -16x + x2 = 0 + -51 -16x + x2 = 0 + -51 Combine like terms: 0 + -51 = -51 -16x + x2 = -51 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 = -51 + 64 Reorder the terms: 64 + -16x + x2 = -51 + 64 Combine like terms: -51 + 64 = 13 64 + -16x + x2 = 13 Factor a perfect square on the left side: (x + -8)(x + -8) = 13 Calculate the square root of the right side: 3.605551275 Break this problem into two subproblems by setting (x + -8) equal to 3.605551275 and -3.605551275.Subproblem 1
x + -8 = 3.605551275 Simplifying x + -8 = 3.605551275 Reorder the terms: -8 + x = 3.605551275 Solving -8 + x = 3.605551275 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 = 3.605551275 + 8 Combine like terms: -8 + 8 = 0 0 + x = 3.605551275 + 8 x = 3.605551275 + 8 Combine like terms: 3.605551275 + 8 = 11.605551275 x = 11.605551275 Simplifying x = 11.605551275Subproblem 2
x + -8 = -3.605551275 Simplifying x + -8 = -3.605551275 Reorder the terms: -8 + x = -3.605551275 Solving -8 + x = -3.605551275 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 = -3.605551275 + 8 Combine like terms: -8 + 8 = 0 0 + x = -3.605551275 + 8 x = -3.605551275 + 8 Combine like terms: -3.605551275 + 8 = 4.394448725 x = 4.394448725 Simplifying x = 4.394448725Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.605551275, 4.394448725}
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