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Simplifying x2 + 16x + -7 = 4 Reorder the terms: -7 + 16x + x2 = 4 Solving -7 + 16x + x2 = 4 Solving for variable 'x'. Reorder the terms: -7 + -4 + 16x + x2 = 4 + -4 Combine like terms: -7 + -4 = -11 -11 + 16x + x2 = 4 + -4 Combine like terms: 4 + -4 = 0 -11 + 16x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '11' to each side of the equation. -11 + 16x + 11 + x2 = 0 + 11 Reorder the terms: -11 + 11 + 16x + x2 = 0 + 11 Combine like terms: -11 + 11 = 0 0 + 16x + x2 = 0 + 11 16x + x2 = 0 + 11 Combine like terms: 0 + 11 = 11 16x + x2 = 11 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 = 11 + 64 Reorder the terms: 64 + 16x + x2 = 11 + 64 Combine like terms: 11 + 64 = 75 64 + 16x + x2 = 75 Factor a perfect square on the left side: (x + 8)(x + 8) = 75 Calculate the square root of the right side: 8.660254038 Break this problem into two subproblems by setting (x + 8) equal to 8.660254038 and -8.660254038.Subproblem 1
x + 8 = 8.660254038 Simplifying x + 8 = 8.660254038 Reorder the terms: 8 + x = 8.660254038 Solving 8 + x = 8.660254038 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 = 8.660254038 + -8 Combine like terms: 8 + -8 = 0 0 + x = 8.660254038 + -8 x = 8.660254038 + -8 Combine like terms: 8.660254038 + -8 = 0.660254038 x = 0.660254038 Simplifying x = 0.660254038Subproblem 2
x + 8 = -8.660254038 Simplifying x + 8 = -8.660254038 Reorder the terms: 8 + x = -8.660254038 Solving 8 + x = -8.660254038 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 = -8.660254038 + -8 Combine like terms: 8 + -8 = 0 0 + x = -8.660254038 + -8 x = -8.660254038 + -8 Combine like terms: -8.660254038 + -8 = -16.660254038 x = -16.660254038 Simplifying x = -16.660254038Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.660254038, -16.660254038}
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