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Simplifying x(x + 1) = 941 Reorder the terms: x(1 + x) = 941 (1 * x + x * x) = 941 (1x + x2) = 941 Solving 1x + x2 = 941 Solving for variable 'x'. Reorder the terms: -941 + 1x + x2 = 941 + -941 Combine like terms: 941 + -941 = 0 -941 + 1x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '941' to each side of the equation. -941 + 1x + 941 + x2 = 0 + 941 Reorder the terms: -941 + 941 + 1x + x2 = 0 + 941 Combine like terms: -941 + 941 = 0 0 + 1x + x2 = 0 + 941 1x + x2 = 0 + 941 Combine like terms: 0 + 941 = 941 1x + x2 = 941 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 = 941 + 0.25 Reorder the terms: 0.25 + x + x2 = 941 + 0.25 Combine like terms: 941 + 0.25 = 941.25 0.25 + x + x2 = 941.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 941.25 Calculate the square root of the right side: 30.679797913 Break this problem into two subproblems by setting (x + 0.5) equal to 30.679797913 and -30.679797913.Subproblem 1
x + 0.5 = 30.679797913 Simplifying x + 0.5 = 30.679797913 Reorder the terms: 0.5 + x = 30.679797913 Solving 0.5 + x = 30.679797913 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 = 30.679797913 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 30.679797913 + -0.5 x = 30.679797913 + -0.5 Combine like terms: 30.679797913 + -0.5 = 30.179797913 x = 30.179797913 Simplifying x = 30.179797913Subproblem 2
x + 0.5 = -30.679797913 Simplifying x + 0.5 = -30.679797913 Reorder the terms: 0.5 + x = -30.679797913 Solving 0.5 + x = -30.679797913 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 = -30.679797913 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -30.679797913 + -0.5 x = -30.679797913 + -0.5 Combine like terms: -30.679797913 + -0.5 = -31.179797913 x = -31.179797913 Simplifying x = -31.179797913Solution
The solution to the problem is based on the solutions from the subproblems. x = {30.179797913, -31.179797913}
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