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Simplifying x2 + -9x + -13 = 0 Reorder the terms: -13 + -9x + x2 = 0 Solving -13 + -9x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '13' to each side of the equation. -13 + -9x + 13 + x2 = 0 + 13 Reorder the terms: -13 + 13 + -9x + x2 = 0 + 13 Combine like terms: -13 + 13 = 0 0 + -9x + x2 = 0 + 13 -9x + x2 = 0 + 13 Combine like terms: 0 + 13 = 13 -9x + x2 = 13 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 = 13 + 20.25 Reorder the terms: 20.25 + -9x + x2 = 13 + 20.25 Combine like terms: 13 + 20.25 = 33.25 20.25 + -9x + x2 = 33.25 Factor a perfect square on the left side: (x + -4.5)(x + -4.5) = 33.25 Calculate the square root of the right side: 5.766281297 Break this problem into two subproblems by setting (x + -4.5) equal to 5.766281297 and -5.766281297.Subproblem 1
x + -4.5 = 5.766281297 Simplifying x + -4.5 = 5.766281297 Reorder the terms: -4.5 + x = 5.766281297 Solving -4.5 + x = 5.766281297 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 = 5.766281297 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = 5.766281297 + 4.5 x = 5.766281297 + 4.5 Combine like terms: 5.766281297 + 4.5 = 10.266281297 x = 10.266281297 Simplifying x = 10.266281297Subproblem 2
x + -4.5 = -5.766281297 Simplifying x + -4.5 = -5.766281297 Reorder the terms: -4.5 + x = -5.766281297 Solving -4.5 + x = -5.766281297 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 = -5.766281297 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = -5.766281297 + 4.5 x = -5.766281297 + 4.5 Combine like terms: -5.766281297 + 4.5 = -1.266281297 x = -1.266281297 Simplifying x = -1.266281297Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.266281297, -1.266281297}
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