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Simplifying x2 + -16x = 51 Reorder the terms: -16x + x2 = 51 Solving -16x + x2 = 51 Solving for variable 'x'. Reorder the terms: -51 + -16x + x2 = 51 + -51 Combine like terms: 51 + -51 = 0 -51 + -16x + x2 = 0 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 = 115 64 + -16x + x2 = 115 Factor a perfect square on the left side: (x + -8)(x + -8) = 115 Calculate the square root of the right side: 10.723805295 Break this problem into two subproblems by setting (x + -8) equal to 10.723805295 and -10.723805295.Subproblem 1
x + -8 = 10.723805295 Simplifying x + -8 = 10.723805295 Reorder the terms: -8 + x = 10.723805295 Solving -8 + x = 10.723805295 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 = 10.723805295 + 8 Combine like terms: -8 + 8 = 0 0 + x = 10.723805295 + 8 x = 10.723805295 + 8 Combine like terms: 10.723805295 + 8 = 18.723805295 x = 18.723805295 Simplifying x = 18.723805295Subproblem 2
x + -8 = -10.723805295 Simplifying x + -8 = -10.723805295 Reorder the terms: -8 + x = -10.723805295 Solving -8 + x = -10.723805295 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 = -10.723805295 + 8 Combine like terms: -8 + 8 = 0 0 + x = -10.723805295 + 8 x = -10.723805295 + 8 Combine like terms: -10.723805295 + 8 = -2.723805295 x = -2.723805295 Simplifying x = -2.723805295Solution
The solution to the problem is based on the solutions from the subproblems. x = {18.723805295, -2.723805295}
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