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Simplifying x(x + 1) = 450 Reorder the terms: x(1 + x) = 450 (1 * x + x * x) = 450 (1x + x2) = 450 Solving 1x + x2 = 450 Solving for variable 'x'. Reorder the terms: -450 + 1x + x2 = 450 + -450 Combine like terms: 450 + -450 = 0 -450 + 1x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '450' to each side of the equation. -450 + 1x + 450 + x2 = 0 + 450 Reorder the terms: -450 + 450 + 1x + x2 = 0 + 450 Combine like terms: -450 + 450 = 0 0 + 1x + x2 = 0 + 450 1x + x2 = 0 + 450 Combine like terms: 0 + 450 = 450 1x + x2 = 450 The x term is 1x. 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 = 450 + 0.25 Reorder the terms: 0.25 + x + x2 = 450 + 0.25 Combine like terms: 450 + 0.25 = 450.25 0.25 + x + x2 = 450.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 450.25 Calculate the square root of the right side: 21.219095174 Break this problem into two subproblems by setting (x + 0.5) equal to 21.219095174 and -21.219095174.Subproblem 1
x + 0.5 = 21.219095174 Simplifying x + 0.5 = 21.219095174 Reorder the terms: 0.5 + x = 21.219095174 Solving 0.5 + x = 21.219095174 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 = 21.219095174 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 21.219095174 + -0.5 x = 21.219095174 + -0.5 Combine like terms: 21.219095174 + -0.5 = 20.719095174 x = 20.719095174 Simplifying x = 20.719095174Subproblem 2
x + 0.5 = -21.219095174 Simplifying x + 0.5 = -21.219095174 Reorder the terms: 0.5 + x = -21.219095174 Solving 0.5 + x = -21.219095174 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 = -21.219095174 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -21.219095174 + -0.5 x = -21.219095174 + -0.5 Combine like terms: -21.219095174 + -0.5 = -21.719095174 x = -21.719095174 Simplifying x = -21.719095174Solution
The solution to the problem is based on the solutions from the subproblems. x = {20.719095174, -21.719095174}
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