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Simplifying x2 + x + -484 = 0 Reorder the terms: -484 + x + x2 = 0 Solving -484 + x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '484' to each side of the equation. -484 + x + 484 + x2 = 0 + 484 Reorder the terms: -484 + 484 + x + x2 = 0 + 484 Combine like terms: -484 + 484 = 0 0 + x + x2 = 0 + 484 x + x2 = 0 + 484 Combine like terms: 0 + 484 = 484 x + x2 = 484 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 = 484 + 0.25 Reorder the terms: 0.25 + x + x2 = 484 + 0.25 Combine like terms: 484 + 0.25 = 484.25 0.25 + x + x2 = 484.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 484.25 Calculate the square root of the right side: 22.005681085 Break this problem into two subproblems by setting (x + 0.5) equal to 22.005681085 and -22.005681085.Subproblem 1
x + 0.5 = 22.005681085 Simplifying x + 0.5 = 22.005681085 Reorder the terms: 0.5 + x = 22.005681085 Solving 0.5 + x = 22.005681085 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 = 22.005681085 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 22.005681085 + -0.5 x = 22.005681085 + -0.5 Combine like terms: 22.005681085 + -0.5 = 21.505681085 x = 21.505681085 Simplifying x = 21.505681085Subproblem 2
x + 0.5 = -22.005681085 Simplifying x + 0.5 = -22.005681085 Reorder the terms: 0.5 + x = -22.005681085 Solving 0.5 + x = -22.005681085 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 = -22.005681085 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -22.005681085 + -0.5 x = -22.005681085 + -0.5 Combine like terms: -22.005681085 + -0.5 = -22.505681085 x = -22.505681085 Simplifying x = -22.505681085Solution
The solution to the problem is based on the solutions from the subproblems. x = {21.505681085, -22.505681085}
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