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Simplifying x2 + x + -3136 = 0 Reorder the terms: -3136 + x + x2 = 0 Solving -3136 + x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '3136' to each side of the equation. -3136 + x + 3136 + x2 = 0 + 3136 Reorder the terms: -3136 + 3136 + x + x2 = 0 + 3136 Combine like terms: -3136 + 3136 = 0 0 + x + x2 = 0 + 3136 x + x2 = 0 + 3136 Combine like terms: 0 + 3136 = 3136 x + x2 = 3136 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 = 3136 + 0.25 Reorder the terms: 0.25 + x + x2 = 3136 + 0.25 Combine like terms: 3136 + 0.25 = 3136.25 0.25 + x + x2 = 3136.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 3136.25 Calculate the square root of the right side: 56.002232098 Break this problem into two subproblems by setting (x + 0.5) equal to 56.002232098 and -56.002232098.Subproblem 1
x + 0.5 = 56.002232098 Simplifying x + 0.5 = 56.002232098 Reorder the terms: 0.5 + x = 56.002232098 Solving 0.5 + x = 56.002232098 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 = 56.002232098 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 56.002232098 + -0.5 x = 56.002232098 + -0.5 Combine like terms: 56.002232098 + -0.5 = 55.502232098 x = 55.502232098 Simplifying x = 55.502232098Subproblem 2
x + 0.5 = -56.002232098 Simplifying x + 0.5 = -56.002232098 Reorder the terms: 0.5 + x = -56.002232098 Solving 0.5 + x = -56.002232098 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 = -56.002232098 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -56.002232098 + -0.5 x = -56.002232098 + -0.5 Combine like terms: -56.002232098 + -0.5 = -56.502232098 x = -56.502232098 Simplifying x = -56.502232098Solution
The solution to the problem is based on the solutions from the subproblems. x = {55.502232098, -56.502232098}
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