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Simplifying x2 + -9x + -67 = 0 Reorder the terms: -67 + -9x + x2 = 0 Solving -67 + -9x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '67' to each side of the equation. -67 + -9x + 67 + x2 = 0 + 67 Reorder the terms: -67 + 67 + -9x + x2 = 0 + 67 Combine like terms: -67 + 67 = 0 0 + -9x + x2 = 0 + 67 -9x + x2 = 0 + 67 Combine like terms: 0 + 67 = 67 -9x + x2 = 67 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 = 67 + 20.25 Reorder the terms: 20.25 + -9x + x2 = 67 + 20.25 Combine like terms: 67 + 20.25 = 87.25 20.25 + -9x + x2 = 87.25 Factor a perfect square on the left side: (x + -4.5)(x + -4.5) = 87.25 Calculate the square root of the right side: 9.340770846 Break this problem into two subproblems by setting (x + -4.5) equal to 9.340770846 and -9.340770846.Subproblem 1
x + -4.5 = 9.340770846 Simplifying x + -4.5 = 9.340770846 Reorder the terms: -4.5 + x = 9.340770846 Solving -4.5 + x = 9.340770846 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 = 9.340770846 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = 9.340770846 + 4.5 x = 9.340770846 + 4.5 Combine like terms: 9.340770846 + 4.5 = 13.840770846 x = 13.840770846 Simplifying x = 13.840770846Subproblem 2
x + -4.5 = -9.340770846 Simplifying x + -4.5 = -9.340770846 Reorder the terms: -4.5 + x = -9.340770846 Solving -4.5 + x = -9.340770846 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 = -9.340770846 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = -9.340770846 + 4.5 x = -9.340770846 + 4.5 Combine like terms: -9.340770846 + 4.5 = -4.840770846 x = -4.840770846 Simplifying x = -4.840770846Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.840770846, -4.840770846}
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