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Simplifying x2 + -1x = 222 Reorder the terms: -1x + x2 = 222 Solving -1x + x2 = 222 Solving for variable 'x'. Reorder the terms: -222 + -1x + x2 = 222 + -222 Combine like terms: 222 + -222 = 0 -222 + -1x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '222' to each side of the equation. -222 + -1x + 222 + x2 = 0 + 222 Reorder the terms: -222 + 222 + -1x + x2 = 0 + 222 Combine like terms: -222 + 222 = 0 0 + -1x + x2 = 0 + 222 -1x + x2 = 0 + 222 Combine like terms: 0 + 222 = 222 -1x + x2 = 222 The x term is -1x. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1x + 0.25 + x2 = 222 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 222 + 0.25 Combine like terms: 222 + 0.25 = 222.25 0.25 + -1x + x2 = 222.25 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 222.25 Calculate the square root of the right side: 14.908051516 Break this problem into two subproblems by setting (x + -0.5) equal to 14.908051516 and -14.908051516.Subproblem 1
x + -0.5 = 14.908051516 Simplifying x + -0.5 = 14.908051516 Reorder the terms: -0.5 + x = 14.908051516 Solving -0.5 + x = 14.908051516 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = 14.908051516 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 14.908051516 + 0.5 x = 14.908051516 + 0.5 Combine like terms: 14.908051516 + 0.5 = 15.408051516 x = 15.408051516 Simplifying x = 15.408051516Subproblem 2
x + -0.5 = -14.908051516 Simplifying x + -0.5 = -14.908051516 Reorder the terms: -0.5 + x = -14.908051516 Solving -0.5 + x = -14.908051516 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = -14.908051516 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -14.908051516 + 0.5 x = -14.908051516 + 0.5 Combine like terms: -14.908051516 + 0.5 = -14.408051516 x = -14.408051516 Simplifying x = -14.408051516Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.408051516, -14.408051516}
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