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Simplifying x2 + 17x + 72.25 = 0 Reorder the terms: 72.25 + 17x + x2 = 0 Solving 72.25 + 17x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-72.25' to each side of the equation. 72.25 + 17x + -72.25 + x2 = 0 + -72.25 Reorder the terms: 72.25 + -72.25 + 17x + x2 = 0 + -72.25 Combine like terms: 72.25 + -72.25 = 0.00 0.00 + 17x + x2 = 0 + -72.25 17x + x2 = 0 + -72.25 Combine like terms: 0 + -72.25 = -72.25 17x + x2 = -72.25 The x term is 17x. Take half its coefficient (8.5). Square it (72.25) and add it to both sides. Add '72.25' to each side of the equation. 17x + 72.25 + x2 = -72.25 + 72.25 Reorder the terms: 72.25 + 17x + x2 = -72.25 + 72.25 Combine like terms: -72.25 + 72.25 = 0.00 72.25 + 17x + x2 = 0.00 Factor a perfect square on the left side: (x + 8.5)(x + 8.5) = 0.00 Calculate the square root of the right side: 0.00 Break this problem into two subproblems by setting (x + 8.5) equal to 0.00 and 0.00.Subproblem 1
x + 8.5 = 0.00 Simplifying x + 8.5 = 0.00 Reorder the terms: 8.5 + x = 0.00 Solving 8.5 + x = 0.00 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8.5' to each side of the equation. 8.5 + -8.5 + x = 0.00 + -8.5 Combine like terms: 8.5 + -8.5 = 0.0 0.0 + x = 0.00 + -8.5 x = 0.00 + -8.5 Combine like terms: 0.00 + -8.5 = -8.5 x = -8.5 Simplifying x = -8.5Subproblem 2
x + 8.5 = 0.00 Simplifying x + 8.5 = 0.00 Reorder the terms: 8.5 + x = 0.00 Solving 8.5 + x = 0.00 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8.5' to each side of the equation. 8.5 + -8.5 + x = 0.00 + -8.5 Combine like terms: 8.5 + -8.5 = 0.0 0.0 + x = 0.00 + -8.5 x = 0.00 + -8.5 Combine like terms: 0.00 + -8.5 = -8.5 x = -8.5 Simplifying x = -8.5Solution
The solution to the problem is based on the solutions from the subproblems. x = {-8.5, -8.5}
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