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Simplifying x2 + 9x + -142 = 0 Reorder the terms: -142 + 9x + x2 = 0 Solving -142 + 9x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '142' to each side of the equation. -142 + 9x + 142 + x2 = 0 + 142 Reorder the terms: -142 + 142 + 9x + x2 = 0 + 142 Combine like terms: -142 + 142 = 0 0 + 9x + x2 = 0 + 142 9x + x2 = 0 + 142 Combine like terms: 0 + 142 = 142 9x + x2 = 142 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 = 142 + 20.25 Reorder the terms: 20.25 + 9x + x2 = 142 + 20.25 Combine like terms: 142 + 20.25 = 162.25 20.25 + 9x + x2 = 162.25 Factor a perfect square on the left side: (x + 4.5)(x + 4.5) = 162.25 Calculate the square root of the right side: 12.737739203 Break this problem into two subproblems by setting (x + 4.5) equal to 12.737739203 and -12.737739203.Subproblem 1
x + 4.5 = 12.737739203 Simplifying x + 4.5 = 12.737739203 Reorder the terms: 4.5 + x = 12.737739203 Solving 4.5 + x = 12.737739203 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 = 12.737739203 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = 12.737739203 + -4.5 x = 12.737739203 + -4.5 Combine like terms: 12.737739203 + -4.5 = 8.237739203 x = 8.237739203 Simplifying x = 8.237739203Subproblem 2
x + 4.5 = -12.737739203 Simplifying x + 4.5 = -12.737739203 Reorder the terms: 4.5 + x = -12.737739203 Solving 4.5 + x = -12.737739203 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 = -12.737739203 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = -12.737739203 + -4.5 x = -12.737739203 + -4.5 Combine like terms: -12.737739203 + -4.5 = -17.237739203 x = -17.237739203 Simplifying x = -17.237739203Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.237739203, -17.237739203}
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