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Simplifying x2 + -3x + -67 = 0 Reorder the terms: -67 + -3x + x2 = 0 Solving -67 + -3x + 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 + -3x + 67 + x2 = 0 + 67 Reorder the terms: -67 + 67 + -3x + x2 = 0 + 67 Combine like terms: -67 + 67 = 0 0 + -3x + x2 = 0 + 67 -3x + x2 = 0 + 67 Combine like terms: 0 + 67 = 67 -3x + x2 = 67 The x term is -3x. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3x + 2.25 + x2 = 67 + 2.25 Reorder the terms: 2.25 + -3x + x2 = 67 + 2.25 Combine like terms: 67 + 2.25 = 69.25 2.25 + -3x + x2 = 69.25 Factor a perfect square on the left side: (x + -1.5)(x + -1.5) = 69.25 Calculate the square root of the right side: 8.321658489 Break this problem into two subproblems by setting (x + -1.5) equal to 8.321658489 and -8.321658489.Subproblem 1
x + -1.5 = 8.321658489 Simplifying x + -1.5 = 8.321658489 Reorder the terms: -1.5 + x = 8.321658489 Solving -1.5 + x = 8.321658489 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = 8.321658489 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 8.321658489 + 1.5 x = 8.321658489 + 1.5 Combine like terms: 8.321658489 + 1.5 = 9.821658489 x = 9.821658489 Simplifying x = 9.821658489Subproblem 2
x + -1.5 = -8.321658489 Simplifying x + -1.5 = -8.321658489 Reorder the terms: -1.5 + x = -8.321658489 Solving -1.5 + x = -8.321658489 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = -8.321658489 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -8.321658489 + 1.5 x = -8.321658489 + 1.5 Combine like terms: -8.321658489 + 1.5 = -6.821658489 x = -6.821658489 Simplifying x = -6.821658489Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.821658489, -6.821658489}
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