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Simplifying 195 = x(x + 1) Reorder the terms: 195 = x(1 + x) 195 = (1 * x + x * x) 195 = (1x + x2) Solving 195 = 1x + x2 Solving for variable 'x'. Reorder the terms: 195 + -1x + -1x2 = 1x + -1x + x2 + -1x2 Combine like terms: 1x + -1x = 0 195 + -1x + -1x2 = 0 + x2 + -1x2 195 + -1x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 195 + -1x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -195 + x + x2 = 0 Move the constant term to the right: Add '195' to each side of the equation. -195 + x + 195 + x2 = 0 + 195 Reorder the terms: -195 + 195 + x + x2 = 0 + 195 Combine like terms: -195 + 195 = 0 0 + x + x2 = 0 + 195 x + x2 = 0 + 195 Combine like terms: 0 + 195 = 195 x + x2 = 195 The x term is x. 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. + 0.25 + x2 = 195 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + x2 = 195 + 0.25 Combine like terms: 195 + 0.25 = 195.25 1.25 + 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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