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Simplifying x2 + 6x + -3125 = 0 Reorder the terms: -3125 + 6x + x2 = 0 Solving -3125 + 6x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '3125' to each side of the equation. -3125 + 6x + 3125 + x2 = 0 + 3125 Reorder the terms: -3125 + 3125 + 6x + x2 = 0 + 3125 Combine like terms: -3125 + 3125 = 0 0 + 6x + x2 = 0 + 3125 6x + x2 = 0 + 3125 Combine like terms: 0 + 3125 = 3125 6x + x2 = 3125 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 = 3125 + 9 Reorder the terms: 9 + 6x + x2 = 3125 + 9 Combine like terms: 3125 + 9 = 3134 9 + 6x + x2 = 3134 Factor a perfect square on the left side: (x + 3)(x + 3) = 3134 Calculate the square root of the right side: 55.982140009 Break this problem into two subproblems by setting (x + 3) equal to 55.982140009 and -55.982140009.Subproblem 1
x + 3 = 55.982140009 Simplifying x + 3 = 55.982140009 Reorder the terms: 3 + x = 55.982140009 Solving 3 + x = 55.982140009 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 = 55.982140009 + -3 Combine like terms: 3 + -3 = 0 0 + x = 55.982140009 + -3 x = 55.982140009 + -3 Combine like terms: 55.982140009 + -3 = 52.982140009 x = 52.982140009 Simplifying x = 52.982140009Subproblem 2
x + 3 = -55.982140009 Simplifying x + 3 = -55.982140009 Reorder the terms: 3 + x = -55.982140009 Solving 3 + x = -55.982140009 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 = -55.982140009 + -3 Combine like terms: 3 + -3 = 0 0 + x = -55.982140009 + -3 x = -55.982140009 + -3 Combine like terms: -55.982140009 + -3 = -58.982140009 x = -58.982140009 Simplifying x = -58.982140009Solution
The solution to the problem is based on the solutions from the subproblems. x = {52.982140009, -58.982140009}
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