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Simplifying x(x + 3) = 191 Reorder the terms: x(3 + x) = 191 (3 * x + x * x) = 191 (3x + x2) = 191 Solving 3x + x2 = 191 Solving for variable 'x'. Reorder the terms: -191 + 3x + x2 = 191 + -191 Combine like terms: 191 + -191 = 0 -191 + 3x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '191' to each side of the equation. -191 + 3x + 191 + x2 = 0 + 191 Reorder the terms: -191 + 191 + 3x + x2 = 0 + 191 Combine like terms: -191 + 191 = 0 0 + 3x + x2 = 0 + 191 3x + x2 = 0 + 191 Combine like terms: 0 + 191 = 191 3x + x2 = 191 The x term is 3x. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3x + 2.25 + x2 = 191 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 191 + 2.25 Combine like terms: 191 + 2.25 = 193.25 2.25 + 3x + x2 = 193.25 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 193.25 Calculate the square root of the right side: 13.901438774 Break this problem into two subproblems by setting (x + 1.5) equal to 13.901438774 and -13.901438774.Subproblem 1
x + 1.5 = 13.901438774 Simplifying x + 1.5 = 13.901438774 Reorder the terms: 1.5 + x = 13.901438774 Solving 1.5 + x = 13.901438774 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = 13.901438774 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 13.901438774 + -1.5 x = 13.901438774 + -1.5 Combine like terms: 13.901438774 + -1.5 = 12.401438774 x = 12.401438774 Simplifying x = 12.401438774Subproblem 2
x + 1.5 = -13.901438774 Simplifying x + 1.5 = -13.901438774 Reorder the terms: 1.5 + x = -13.901438774 Solving 1.5 + x = -13.901438774 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = -13.901438774 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -13.901438774 + -1.5 x = -13.901438774 + -1.5 Combine like terms: -13.901438774 + -1.5 = -15.401438774 x = -15.401438774 Simplifying x = -15.401438774Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.401438774, -15.401438774}
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