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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 = -4.394448725 x = -4.394448725 Simplifying x = -4.394448725Subproblem 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 = -11.605551275 x = -11.605551275 Simplifying x = -11.605551275Solution
The solution to the problem is based on the solutions from the subproblems. x = {-4.394448725, -11.605551275}
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