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Simplifying x + x2 = 1224 Solving x + x2 = 1224 Solving for variable 'x'. Reorder the terms: -1224 + x + x2 = 1224 + -1224 Combine like terms: 1224 + -1224 = 0 -1224 + x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '1224' to each side of the equation. -1224 + x + 1224 + x2 = 0 + 1224 Reorder the terms: -1224 + 1224 + x + x2 = 0 + 1224 Combine like terms: -1224 + 1224 = 0 0 + x + x2 = 0 + 1224 x + x2 = 0 + 1224 Combine like terms: 0 + 1224 = 1224 x + x2 = 1224 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 = 1224 + 0.25 Reorder the terms: 0.25 + x + x2 = 1224 + 0.25 Combine like terms: 1224 + 0.25 = 1224.25 0.25 + x + x2 = 1224.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 1224.25 Calculate the square root of the right side: 34.989284074 Break this problem into two subproblems by setting (x + 0.5) equal to 34.989284074 and -34.989284074.Subproblem 1
x + 0.5 = 34.989284074 Simplifying x + 0.5 = 34.989284074 Reorder the terms: 0.5 + x = 34.989284074 Solving 0.5 + x = 34.989284074 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 = 34.989284074 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 34.989284074 + -0.5 x = 34.989284074 + -0.5 Combine like terms: 34.989284074 + -0.5 = 34.489284074 x = 34.489284074 Simplifying x = 34.489284074Subproblem 2
x + 0.5 = -34.989284074 Simplifying x + 0.5 = -34.989284074 Reorder the terms: 0.5 + x = -34.989284074 Solving 0.5 + x = -34.989284074 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 = -34.989284074 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -34.989284074 + -0.5 x = -34.989284074 + -0.5 Combine like terms: -34.989284074 + -0.5 = -35.489284074 x = -35.489284074 Simplifying x = -35.489284074Solution
The solution to the problem is based on the solutions from the subproblems. x = {34.489284074, -35.489284074}
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