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Simplifying x2 + 8x + 16 = 16.9 Reorder the terms: 16 + 8x + x2 = 16.9 Solving 16 + 8x + x2 = 16.9 Solving for variable 'x'. Reorder the terms: 16 + -16.9 + 8x + x2 = 16.9 + -16.9 Combine like terms: 16 + -16.9 = -0.9 -0.9 + 8x + x2 = 16.9 + -16.9 Combine like terms: 16.9 + -16.9 = 0.0 -0.9 + 8x + x2 = 0.0 Begin completing the square. Move the constant term to the right: Add '0.9' to each side of the equation. -0.9 + 8x + 0.9 + x2 = 0.0 + 0.9 Reorder the terms: -0.9 + 0.9 + 8x + x2 = 0.0 + 0.9 Combine like terms: -0.9 + 0.9 = 0.0 0.0 + 8x + x2 = 0.0 + 0.9 8x + x2 = 0.0 + 0.9 Combine like terms: 0.0 + 0.9 = 0.9 8x + x2 = 0.9 The x term is 8x. Take half its coefficient (4). Square it (16) and add it to both sides. Add '16' to each side of the equation. 8x + 16 + x2 = 0.9 + 16 Reorder the terms: 16 + 8x + x2 = 0.9 + 16 Combine like terms: 0.9 + 16 = 16.9 16 + 8x + x2 = 16.9 Factor a perfect square on the left side: (x + 4)(x + 4) = 16.9 Calculate the square root of the right side: 4.110960958 Break this problem into two subproblems by setting (x + 4) equal to 4.110960958 and -4.110960958.Subproblem 1
x + 4 = 4.110960958 Simplifying x + 4 = 4.110960958 Reorder the terms: 4 + x = 4.110960958 Solving 4 + x = 4.110960958 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = 4.110960958 + -4 Combine like terms: 4 + -4 = 0 0 + x = 4.110960958 + -4 x = 4.110960958 + -4 Combine like terms: 4.110960958 + -4 = 0.110960958 x = 0.110960958 Simplifying x = 0.110960958Subproblem 2
x + 4 = -4.110960958 Simplifying x + 4 = -4.110960958 Reorder the terms: 4 + x = -4.110960958 Solving 4 + x = -4.110960958 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = -4.110960958 + -4 Combine like terms: 4 + -4 = 0 0 + x = -4.110960958 + -4 x = -4.110960958 + -4 Combine like terms: -4.110960958 + -4 = -8.110960958 x = -8.110960958 Simplifying x = -8.110960958Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.110960958, -8.110960958}
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