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Simplifying x2 + 3x = 260 Reorder the terms: 3x + x2 = 260 Solving 3x + x2 = 260 Solving for variable 'x'. Reorder the terms: -260 + 3x + x2 = 260 + -260 Combine like terms: 260 + -260 = 0 -260 + 3x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '260' to each side of the equation. -260 + 3x + 260 + x2 = 0 + 260 Reorder the terms: -260 + 260 + 3x + x2 = 0 + 260 Combine like terms: -260 + 260 = 0 0 + 3x + x2 = 0 + 260 3x + x2 = 0 + 260 Combine like terms: 0 + 260 = 260 3x + x2 = 260 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 = 260 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 260 + 2.25 Combine like terms: 260 + 2.25 = 262.25 2.25 + 3x + x2 = 262.25 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 262.25 Calculate the square root of the right side: 16.194134741 Break this problem into two subproblems by setting (x + 1.5) equal to 16.194134741 and -16.194134741.Subproblem 1
x + 1.5 = 16.194134741 Simplifying x + 1.5 = 16.194134741 Reorder the terms: 1.5 + x = 16.194134741 Solving 1.5 + x = 16.194134741 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 = 16.194134741 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 16.194134741 + -1.5 x = 16.194134741 + -1.5 Combine like terms: 16.194134741 + -1.5 = 14.694134741 x = 14.694134741 Simplifying x = 14.694134741Subproblem 2
x + 1.5 = -16.194134741 Simplifying x + 1.5 = -16.194134741 Reorder the terms: 1.5 + x = -16.194134741 Solving 1.5 + x = -16.194134741 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 = -16.194134741 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -16.194134741 + -1.5 x = -16.194134741 + -1.5 Combine like terms: -16.194134741 + -1.5 = -17.694134741 x = -17.694134741 Simplifying x = -17.694134741Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.694134741, -17.694134741}
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