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Simplifying x2 + x = 700 Reorder the terms: x + x2 = 700 Solving x + x2 = 700 Solving for variable 'x'. Reorder the terms: -700 + x + x2 = 700 + -700 Combine like terms: 700 + -700 = 0 -700 + x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '700' to each side of the equation. -700 + x + 700 + x2 = 0 + 700 Reorder the terms: -700 + 700 + x + x2 = 0 + 700 Combine like terms: -700 + 700 = 0 0 + x + x2 = 0 + 700 x + x2 = 0 + 700 Combine like terms: 0 + 700 = 700 x + x2 = 700 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 = 700 + 0.25 Reorder the terms: 0.25 + x + x2 = 700 + 0.25 Combine like terms: 700 + 0.25 = 700.25 0.25 + x + x2 = 700.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 700.25 Calculate the square root of the right side: 26.462237245 Break this problem into two subproblems by setting (x + 0.5) equal to 26.462237245 and -26.462237245.Subproblem 1
x + 0.5 = 26.462237245 Simplifying x + 0.5 = 26.462237245 Reorder the terms: 0.5 + x = 26.462237245 Solving 0.5 + x = 26.462237245 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 = 26.462237245 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 26.462237245 + -0.5 x = 26.462237245 + -0.5 Combine like terms: 26.462237245 + -0.5 = 25.962237245 x = 25.962237245 Simplifying x = 25.962237245Subproblem 2
x + 0.5 = -26.462237245 Simplifying x + 0.5 = -26.462237245 Reorder the terms: 0.5 + x = -26.462237245 Solving 0.5 + x = -26.462237245 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 = -26.462237245 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -26.462237245 + -0.5 x = -26.462237245 + -0.5 Combine like terms: -26.462237245 + -0.5 = -26.962237245 x = -26.962237245 Simplifying x = -26.962237245Solution
The solution to the problem is based on the solutions from the subproblems. x = {25.962237245, -26.962237245}
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