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Simplifying x2 + -3x + -300 = 0 Reorder the terms: -300 + -3x + x2 = 0 Solving -300 + -3x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '300' to each side of the equation. -300 + -3x + 300 + x2 = 0 + 300 Reorder the terms: -300 + 300 + -3x + x2 = 0 + 300 Combine like terms: -300 + 300 = 0 0 + -3x + x2 = 0 + 300 -3x + x2 = 0 + 300 Combine like terms: 0 + 300 = 300 -3x + x2 = 300 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 = 300 + 2.25 Reorder the terms: 2.25 + -3x + x2 = 300 + 2.25 Combine like terms: 300 + 2.25 = 302.25 2.25 + -3x + x2 = 302.25 Factor a perfect square on the left side: (x + -1.5)(x + -1.5) = 302.25 Calculate the square root of the right side: 17.385338651 Break this problem into two subproblems by setting (x + -1.5) equal to 17.385338651 and -17.385338651.Subproblem 1
x + -1.5 = 17.385338651 Simplifying x + -1.5 = 17.385338651 Reorder the terms: -1.5 + x = 17.385338651 Solving -1.5 + x = 17.385338651 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 = 17.385338651 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 17.385338651 + 1.5 x = 17.385338651 + 1.5 Combine like terms: 17.385338651 + 1.5 = 18.885338651 x = 18.885338651 Simplifying x = 18.885338651Subproblem 2
x + -1.5 = -17.385338651 Simplifying x + -1.5 = -17.385338651 Reorder the terms: -1.5 + x = -17.385338651 Solving -1.5 + x = -17.385338651 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 = -17.385338651 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -17.385338651 + 1.5 x = -17.385338651 + 1.5 Combine like terms: -17.385338651 + 1.5 = -15.885338651 x = -15.885338651 Simplifying x = -15.885338651Solution
The solution to the problem is based on the solutions from the subproblems. x = {18.885338651, -15.885338651}
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