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Simplifying x2 + 8.5x + 18 = 0 Reorder the terms: 18 + 8.5x + x2 = 0 Solving 18 + 8.5x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-18' to each side of the equation. 18 + 8.5x + -18 + x2 = 0 + -18 Reorder the terms: 18 + -18 + 8.5x + x2 = 0 + -18 Combine like terms: 18 + -18 = 0 0 + 8.5x + x2 = 0 + -18 8.5x + x2 = 0 + -18 Combine like terms: 0 + -18 = -18 8.5x + x2 = -18 The x term is 8.5x. Take half its coefficient (4.25). Square it (18.0625) and add it to both sides. Add '18.0625' to each side of the equation. 8.5x + 18.0625 + x2 = -18 + 18.0625 Reorder the terms: 18.0625 + 8.5x + x2 = -18 + 18.0625 Combine like terms: -18 + 18.0625 = 0.0625 18.0625 + 8.5x + x2 = 0.0625 Factor a perfect square on the left side: (x + 4.25)(x + 4.25) = 0.0625 Calculate the square root of the right side: 0.25 Break this problem into two subproblems by setting (x + 4.25) equal to 0.25 and -0.25.Subproblem 1
x + 4.25 = 0.25 Simplifying x + 4.25 = 0.25 Reorder the terms: 4.25 + x = 0.25 Solving 4.25 + x = 0.25 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.25' to each side of the equation. 4.25 + -4.25 + x = 0.25 + -4.25 Combine like terms: 4.25 + -4.25 = 0.00 0.00 + x = 0.25 + -4.25 x = 0.25 + -4.25 Combine like terms: 0.25 + -4.25 = -4 x = -4 Simplifying x = -4Subproblem 2
x + 4.25 = -0.25 Simplifying x + 4.25 = -0.25 Reorder the terms: 4.25 + x = -0.25 Solving 4.25 + x = -0.25 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.25' to each side of the equation. 4.25 + -4.25 + x = -0.25 + -4.25 Combine like terms: 4.25 + -4.25 = 0.00 0.00 + x = -0.25 + -4.25 x = -0.25 + -4.25 Combine like terms: -0.25 + -4.25 = -4.5 x = -4.5 Simplifying x = -4.5Solution
The solution to the problem is based on the solutions from the subproblems. x = {-4, -4.5}
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