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Simplifying x2 + -11x + -67 = 0 Reorder the terms: -67 + -11x + x2 = 0 Solving -67 + -11x + 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 + -11x + 67 + x2 = 0 + 67 Reorder the terms: -67 + 67 + -11x + x2 = 0 + 67 Combine like terms: -67 + 67 = 0 0 + -11x + x2 = 0 + 67 -11x + x2 = 0 + 67 Combine like terms: 0 + 67 = 67 -11x + x2 = 67 The x term is -11x. Take half its coefficient (-5.5). Square it (30.25) and add it to both sides. Add '30.25' to each side of the equation. -11x + 30.25 + x2 = 67 + 30.25 Reorder the terms: 30.25 + -11x + x2 = 67 + 30.25 Combine like terms: 67 + 30.25 = 97.25 30.25 + -11x + x2 = 97.25 Factor a perfect square on the left side: (x + -5.5)(x + -5.5) = 97.25 Calculate the square root of the right side: 9.861541462 Break this problem into two subproblems by setting (x + -5.5) equal to 9.861541462 and -9.861541462.Subproblem 1
x + -5.5 = 9.861541462 Simplifying x + -5.5 = 9.861541462 Reorder the terms: -5.5 + x = 9.861541462 Solving -5.5 + x = 9.861541462 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + x = 9.861541462 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + x = 9.861541462 + 5.5 x = 9.861541462 + 5.5 Combine like terms: 9.861541462 + 5.5 = 15.361541462 x = 15.361541462 Simplifying x = 15.361541462Subproblem 2
x + -5.5 = -9.861541462 Simplifying x + -5.5 = -9.861541462 Reorder the terms: -5.5 + x = -9.861541462 Solving -5.5 + x = -9.861541462 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + x = -9.861541462 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + x = -9.861541462 + 5.5 x = -9.861541462 + 5.5 Combine like terms: -9.861541462 + 5.5 = -4.361541462 x = -4.361541462 Simplifying x = -4.361541462Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.361541462, -4.361541462}
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