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Simplifying x2 + -1x + -300 = 0 Reorder the terms: -300 + -1x + x2 = 0 Solving -300 + -1x + 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 + -1x + 300 + x2 = 0 + 300 Reorder the terms: -300 + 300 + -1x + x2 = 0 + 300 Combine like terms: -300 + 300 = 0 0 + -1x + x2 = 0 + 300 -1x + x2 = 0 + 300 Combine like terms: 0 + 300 = 300 -1x + x2 = 300 The x term is -1x. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1x + 0.25 + x2 = 300 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 300 + 0.25 Combine like terms: 300 + 0.25 = 300.25 0.25 + -1x + x2 = 300.25 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 300.25 Calculate the square root of the right side: 17.327723451 Break this problem into two subproblems by setting (x + -0.5) equal to 17.327723451 and -17.327723451.Subproblem 1
x + -0.5 = 17.327723451 Simplifying x + -0.5 = 17.327723451 Reorder the terms: -0.5 + x = 17.327723451 Solving -0.5 + x = 17.327723451 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = 17.327723451 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 17.327723451 + 0.5 x = 17.327723451 + 0.5 Combine like terms: 17.327723451 + 0.5 = 17.827723451 x = 17.827723451 Simplifying x = 17.827723451Subproblem 2
x + -0.5 = -17.327723451 Simplifying x + -0.5 = -17.327723451 Reorder the terms: -0.5 + x = -17.327723451 Solving -0.5 + x = -17.327723451 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = -17.327723451 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -17.327723451 + 0.5 x = -17.327723451 + 0.5 Combine like terms: -17.327723451 + 0.5 = -16.827723451 x = -16.827723451 Simplifying x = -16.827723451Solution
The solution to the problem is based on the solutions from the subproblems. x = {17.827723451, -16.827723451}
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