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Simplifying x2 + 3x = 363 Reorder the terms: 3x + x2 = 363 Solving 3x + x2 = 363 Solving for variable 'x'. Reorder the terms: -363 + 3x + x2 = 363 + -363 Combine like terms: 363 + -363 = 0 -363 + 3x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '363' to each side of the equation. -363 + 3x + 363 + x2 = 0 + 363 Reorder the terms: -363 + 363 + 3x + x2 = 0 + 363 Combine like terms: -363 + 363 = 0 0 + 3x + x2 = 0 + 363 3x + x2 = 0 + 363 Combine like terms: 0 + 363 = 363 3x + x2 = 363 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 = 363 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 363 + 2.25 Combine like terms: 363 + 2.25 = 365.25 2.25 + 3x + x2 = 365.25 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 365.25 Calculate the square root of the right side: 19.111514854 Break this problem into two subproblems by setting (x + 1.5) equal to 19.111514854 and -19.111514854.Subproblem 1
x + 1.5 = 19.111514854 Simplifying x + 1.5 = 19.111514854 Reorder the terms: 1.5 + x = 19.111514854 Solving 1.5 + x = 19.111514854 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 = 19.111514854 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 19.111514854 + -1.5 x = 19.111514854 + -1.5 Combine like terms: 19.111514854 + -1.5 = 17.611514854 x = 17.611514854 Simplifying x = 17.611514854Subproblem 2
x + 1.5 = -19.111514854 Simplifying x + 1.5 = -19.111514854 Reorder the terms: 1.5 + x = -19.111514854 Solving 1.5 + x = -19.111514854 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 = -19.111514854 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -19.111514854 + -1.5 x = -19.111514854 + -1.5 Combine like terms: -19.111514854 + -1.5 = -20.611514854 x = -20.611514854 Simplifying x = -20.611514854Solution
The solution to the problem is based on the solutions from the subproblems. x = {17.611514854, -20.611514854}
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