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Simplifying x2 + 9x + -1062 = 0 Reorder the terms: -1062 + 9x + x2 = 0 Solving -1062 + 9x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '1062' to each side of the equation. -1062 + 9x + 1062 + x2 = 0 + 1062 Reorder the terms: -1062 + 1062 + 9x + x2 = 0 + 1062 Combine like terms: -1062 + 1062 = 0 0 + 9x + x2 = 0 + 1062 9x + x2 = 0 + 1062 Combine like terms: 0 + 1062 = 1062 9x + x2 = 1062 The x term is 9x. Take half its coefficient (4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. 9x + 20.25 + x2 = 1062 + 20.25 Reorder the terms: 20.25 + 9x + x2 = 1062 + 20.25 Combine like terms: 1062 + 20.25 = 1082.25 20.25 + 9x + x2 = 1082.25 Factor a perfect square on the left side: (x + 4.5)(x + 4.5) = 1082.25 Calculate the square root of the right side: 32.897568299 Break this problem into two subproblems by setting (x + 4.5) equal to 32.897568299 and -32.897568299.Subproblem 1
x + 4.5 = 32.897568299 Simplifying x + 4.5 = 32.897568299 Reorder the terms: 4.5 + x = 32.897568299 Solving 4.5 + x = 32.897568299 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + x = 32.897568299 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = 32.897568299 + -4.5 x = 32.897568299 + -4.5 Combine like terms: 32.897568299 + -4.5 = 28.397568299 x = 28.397568299 Simplifying x = 28.397568299Subproblem 2
x + 4.5 = -32.897568299 Simplifying x + 4.5 = -32.897568299 Reorder the terms: 4.5 + x = -32.897568299 Solving 4.5 + x = -32.897568299 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + x = -32.897568299 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = -32.897568299 + -4.5 x = -32.897568299 + -4.5 Combine like terms: -32.897568299 + -4.5 = -37.397568299 x = -37.397568299 Simplifying x = -37.397568299Solution
The solution to the problem is based on the solutions from the subproblems. x = {28.397568299, -37.397568299}
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