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Simplifying x2 + 6x + -600 = 0 Reorder the terms: -600 + 6x + x2 = 0 Solving -600 + 6x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '600' to each side of the equation. -600 + 6x + 600 + x2 = 0 + 600 Reorder the terms: -600 + 600 + 6x + x2 = 0 + 600 Combine like terms: -600 + 600 = 0 0 + 6x + x2 = 0 + 600 6x + x2 = 0 + 600 Combine like terms: 0 + 600 = 600 6x + x2 = 600 The x term is 6x. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6x + 9 + x2 = 600 + 9 Reorder the terms: 9 + 6x + x2 = 600 + 9 Combine like terms: 600 + 9 = 609 9 + 6x + x2 = 609 Factor a perfect square on the left side: (x + 3)(x + 3) = 609 Calculate the square root of the right side: 24.677925359 Break this problem into two subproblems by setting (x + 3) equal to 24.677925359 and -24.677925359.Subproblem 1
x + 3 = 24.677925359 Simplifying x + 3 = 24.677925359 Reorder the terms: 3 + x = 24.677925359 Solving 3 + x = 24.677925359 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 24.677925359 + -3 Combine like terms: 3 + -3 = 0 0 + x = 24.677925359 + -3 x = 24.677925359 + -3 Combine like terms: 24.677925359 + -3 = 21.677925359 x = 21.677925359 Simplifying x = 21.677925359Subproblem 2
x + 3 = -24.677925359 Simplifying x + 3 = -24.677925359 Reorder the terms: 3 + x = -24.677925359 Solving 3 + x = -24.677925359 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = -24.677925359 + -3 Combine like terms: 3 + -3 = 0 0 + x = -24.677925359 + -3 x = -24.677925359 + -3 Combine like terms: -24.677925359 + -3 = -27.677925359 x = -27.677925359 Simplifying x = -27.677925359Solution
The solution to the problem is based on the solutions from the subproblems. x = {21.677925359, -27.677925359}
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