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Simplifying x2 + -7x + -222 = 0 Reorder the terms: -222 + -7x + x2 = 0 Solving -222 + -7x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '222' to each side of the equation. -222 + -7x + 222 + x2 = 0 + 222 Reorder the terms: -222 + 222 + -7x + x2 = 0 + 222 Combine like terms: -222 + 222 = 0 0 + -7x + x2 = 0 + 222 -7x + x2 = 0 + 222 Combine like terms: 0 + 222 = 222 -7x + x2 = 222 The x term is -7x. Take half its coefficient (-3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. -7x + 12.25 + x2 = 222 + 12.25 Reorder the terms: 12.25 + -7x + x2 = 222 + 12.25 Combine like terms: 222 + 12.25 = 234.25 12.25 + -7x + x2 = 234.25 Factor a perfect square on the left side: (x + -3.5)(x + -3.5) = 234.25 Calculate the square root of the right side: 15.305227865 Break this problem into two subproblems by setting (x + -3.5) equal to 15.305227865 and -15.305227865.Subproblem 1
x + -3.5 = 15.305227865 Simplifying x + -3.5 = 15.305227865 Reorder the terms: -3.5 + x = 15.305227865 Solving -3.5 + x = 15.305227865 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x = 15.305227865 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = 15.305227865 + 3.5 x = 15.305227865 + 3.5 Combine like terms: 15.305227865 + 3.5 = 18.805227865 x = 18.805227865 Simplifying x = 18.805227865Subproblem 2
x + -3.5 = -15.305227865 Simplifying x + -3.5 = -15.305227865 Reorder the terms: -3.5 + x = -15.305227865 Solving -3.5 + x = -15.305227865 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x = -15.305227865 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = -15.305227865 + 3.5 x = -15.305227865 + 3.5 Combine like terms: -15.305227865 + 3.5 = -11.805227865 x = -11.805227865 Simplifying x = -11.805227865Solution
The solution to the problem is based on the solutions from the subproblems. x = {18.805227865, -11.805227865}
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