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Simplifying x2 + x + -3135 = 0 Reorder the terms: -3135 + x + x2 = 0 Solving -3135 + x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '3135' to each side of the equation. -3135 + x + 3135 + x2 = 0 + 3135 Reorder the terms: -3135 + 3135 + x + x2 = 0 + 3135 Combine like terms: -3135 + 3135 = 0 0 + x + x2 = 0 + 3135 x + x2 = 0 + 3135 Combine like terms: 0 + 3135 = 3135 x + x2 = 3135 The x term is x. 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. x + 0.25 + x2 = 3135 + 0.25 Reorder the terms: 0.25 + x + x2 = 3135 + 0.25 Combine like terms: 3135 + 0.25 = 3135.25 0.25 + x + x2 = 3135.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 3135.25 Calculate the square root of the right side: 55.993303171 Break this problem into two subproblems by setting (x + 0.5) equal to 55.993303171 and -55.993303171.Subproblem 1
x + 0.5 = 55.993303171 Simplifying x + 0.5 = 55.993303171 Reorder the terms: 0.5 + x = 55.993303171 Solving 0.5 + x = 55.993303171 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 = 55.993303171 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 55.993303171 + -0.5 x = 55.993303171 + -0.5 Combine like terms: 55.993303171 + -0.5 = 55.493303171 x = 55.493303171 Simplifying x = 55.493303171Subproblem 2
x + 0.5 = -55.993303171 Simplifying x + 0.5 = -55.993303171 Reorder the terms: 0.5 + x = -55.993303171 Solving 0.5 + x = -55.993303171 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 = -55.993303171 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -55.993303171 + -0.5 x = -55.993303171 + -0.5 Combine like terms: -55.993303171 + -0.5 = -56.493303171 x = -56.493303171 Simplifying x = -56.493303171Solution
The solution to the problem is based on the solutions from the subproblems. x = {55.493303171, -56.493303171}
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