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Simplifying x2 + 3x = 201 Reorder the terms: 3x + x2 = 201 Solving 3x + x2 = 201 Solving for variable 'x'. Reorder the terms: -201 + 3x + x2 = 201 + -201 Combine like terms: 201 + -201 = 0 -201 + 3x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '201' to each side of the equation. -201 + 3x + 201 + x2 = 0 + 201 Reorder the terms: -201 + 201 + 3x + x2 = 0 + 201 Combine like terms: -201 + 201 = 0 0 + 3x + x2 = 0 + 201 3x + x2 = 0 + 201 Combine like terms: 0 + 201 = 201 3x + x2 = 201 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 = 201 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 201 + 2.25 Combine like terms: 201 + 2.25 = 203.25 2.25 + 3x + x2 = 203.25 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 203.25 Calculate the square root of the right side: 14.256577429 Break this problem into two subproblems by setting (x + 1.5) equal to 14.256577429 and -14.256577429.Subproblem 1
x + 1.5 = 14.256577429 Simplifying x + 1.5 = 14.256577429 Reorder the terms: 1.5 + x = 14.256577429 Solving 1.5 + x = 14.256577429 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 = 14.256577429 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 14.256577429 + -1.5 x = 14.256577429 + -1.5 Combine like terms: 14.256577429 + -1.5 = 12.756577429 x = 12.756577429 Simplifying x = 12.756577429Subproblem 2
x + 1.5 = -14.256577429 Simplifying x + 1.5 = -14.256577429 Reorder the terms: 1.5 + x = -14.256577429 Solving 1.5 + x = -14.256577429 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 = -14.256577429 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -14.256577429 + -1.5 x = -14.256577429 + -1.5 Combine like terms: -14.256577429 + -1.5 = -15.756577429 x = -15.756577429 Simplifying x = -15.756577429Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.756577429, -15.756577429}
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