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Simplifying x(x + 1) = 195 Reorder the terms: x(1 + x) = 195 (1 * x + x * x) = 195 (1x + x2) = 195 Solving 1x + x2 = 195 Solving for variable 'x'. Reorder the terms: -195 + 1x + x2 = 195 + -195 Combine like terms: 195 + -195 = 0 -195 + 1x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '195' to each side of the equation. -195 + 1x + 195 + x2 = 0 + 195 Reorder the terms: -195 + 195 + 1x + x2 = 0 + 195 Combine like terms: -195 + 195 = 0 0 + 1x + x2 = 0 + 195 1x + x2 = 0 + 195 Combine like terms: 0 + 195 = 195 1x + x2 = 195 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 = 195 + 0.25 Reorder the terms: 0.25 + x + x2 = 195 + 0.25 Combine like terms: 195 + 0.25 = 195.25 0.25 + x + x2 = 195.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 195.25 Calculate the square root of the right side: 13.973188612 Break this problem into two subproblems by setting (x + 0.5) equal to 13.973188612 and -13.973188612.Subproblem 1
x + 0.5 = 13.973188612 Simplifying x + 0.5 = 13.973188612 Reorder the terms: 0.5 + x = 13.973188612 Solving 0.5 + x = 13.973188612 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 = 13.973188612 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 13.973188612 + -0.5 x = 13.973188612 + -0.5 Combine like terms: 13.973188612 + -0.5 = 13.473188612 x = 13.473188612 Simplifying x = 13.473188612Subproblem 2
x + 0.5 = -13.973188612 Simplifying x + 0.5 = -13.973188612 Reorder the terms: 0.5 + x = -13.973188612 Solving 0.5 + x = -13.973188612 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 = -13.973188612 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -13.973188612 + -0.5 x = -13.973188612 + -0.5 Combine like terms: -13.973188612 + -0.5 = -14.473188612 x = -14.473188612 Simplifying x = -14.473188612Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.473188612, -14.473188612}
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