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Simplifying x2 + 16x + 1 = -7 Reorder the terms: 1 + 16x + x2 = -7 Solving 1 + 16x + x2 = -7 Solving for variable 'x'. Reorder the terms: 1 + 7 + 16x + x2 = -7 + 7 Combine like terms: 1 + 7 = 8 8 + 16x + x2 = -7 + 7 Combine like terms: -7 + 7 = 0 8 + 16x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-8' to each side of the equation. 8 + 16x + -8 + x2 = 0 + -8 Reorder the terms: 8 + -8 + 16x + x2 = 0 + -8 Combine like terms: 8 + -8 = 0 0 + 16x + x2 = 0 + -8 16x + x2 = 0 + -8 Combine like terms: 0 + -8 = -8 16x + x2 = -8 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 = -8 + 64 Reorder the terms: 64 + 16x + x2 = -8 + 64 Combine like terms: -8 + 64 = 56 64 + 16x + x2 = 56 Factor a perfect square on the left side: (x + 8)(x + 8) = 56 Calculate the square root of the right side: 7.483314774 Break this problem into two subproblems by setting (x + 8) equal to 7.483314774 and -7.483314774.Subproblem 1
x + 8 = 7.483314774 Simplifying x + 8 = 7.483314774 Reorder the terms: 8 + x = 7.483314774 Solving 8 + x = 7.483314774 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 = 7.483314774 + -8 Combine like terms: 8 + -8 = 0 0 + x = 7.483314774 + -8 x = 7.483314774 + -8 Combine like terms: 7.483314774 + -8 = -0.516685226 x = -0.516685226 Simplifying x = -0.516685226Subproblem 2
x + 8 = -7.483314774 Simplifying x + 8 = -7.483314774 Reorder the terms: 8 + x = -7.483314774 Solving 8 + x = -7.483314774 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 = -7.483314774 + -8 Combine like terms: 8 + -8 = 0 0 + x = -7.483314774 + -8 x = -7.483314774 + -8 Combine like terms: -7.483314774 + -8 = -15.483314774 x = -15.483314774 Simplifying x = -15.483314774Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.516685226, -15.483314774}
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