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Simplifying x(x + 1) = 212 Reorder the terms: x(1 + x) = 212 (1 * x + x * x) = 212 (1x + x2) = 212 Solving 1x + x2 = 212 Solving for variable 'x'. Reorder the terms: -212 + 1x + x2 = 212 + -212 Combine like terms: 212 + -212 = 0 -212 + 1x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '212' to each side of the equation. -212 + 1x + 212 + x2 = 0 + 212 Reorder the terms: -212 + 212 + 1x + x2 = 0 + 212 Combine like terms: -212 + 212 = 0 0 + 1x + x2 = 0 + 212 1x + x2 = 0 + 212 Combine like terms: 0 + 212 = 212 1x + x2 = 212 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. x + 0.25 + x2 = 212 + 0.25 Reorder the terms: 0.25 + x + x2 = 212 + 0.25 Combine like terms: 212 + 0.25 = 212.25 0.25 + x + x2 = 212.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 212.25 Calculate the square root of the right side: 14.568802284 Break this problem into two subproblems by setting (x + 0.5) equal to 14.568802284 and -14.568802284.Subproblem 1
x + 0.5 = 14.568802284 Simplifying x + 0.5 = 14.568802284 Reorder the terms: 0.5 + x = 14.568802284 Solving 0.5 + x = 14.568802284 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 = 14.568802284 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 14.568802284 + -0.5 x = 14.568802284 + -0.5 Combine like terms: 14.568802284 + -0.5 = 14.068802284 x = 14.068802284 Simplifying x = 14.068802284Subproblem 2
x + 0.5 = -14.568802284 Simplifying x + 0.5 = -14.568802284 Reorder the terms: 0.5 + x = -14.568802284 Solving 0.5 + x = -14.568802284 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 = -14.568802284 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -14.568802284 + -0.5 x = -14.568802284 + -0.5 Combine like terms: -14.568802284 + -0.5 = -15.068802284 x = -15.068802284 Simplifying x = -15.068802284Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.068802284, -15.068802284}
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